GUIDE BOOK: CDC Optional Mathematics

AMBIK BARAL, Ghanashyam Adhikari, Mar 20, 2023

In this book, first of all I will solve all the questions from optional mathematics CDC book of Nepal. Later I will include all SEE/SLC old questions solution. It will be helpful for some needy students of Nepal.

Table of Contents

  1. Function
    1. Unit 1.1.1 (a) Function
    2. Unit: 1.1.1 (b)Function
    3. Unit1.1.2 : Function
    4. Unit 1.1.3: Function
  2. Polynomial
    1. Unit 1.2.1: Polynomial
    2. Unit: 1.2.2 : Synthetic Division
    3. Unit 1.2.3(A): Some theorems on polynomials
    4. Unit 1.2.3 (B) : Factor theorem
  3. Trigonometry
    1. Multiple Angles
    2. Sub-Multiple Angles
    3. Transformation Of Trigonometric Formula
    4. Conditional Trigonometric Identities
    5. Trigonometric Equations
  4. Statistics
    1. Statistics-Class-10-Opt. Maths (2+4+4=10 Marks)

1.

Function

  • 1. Unit 1.1.1 (a) Function
  • 2. Unit: 1.1.1 (b)Function
  • 3. Unit1.1.2 : Function
  • 4. Unit 1.1.3: Function

1.1.

Unit 1.1.1 (a) Function

1. (a) Define linear function with example.[br][br]Solution:[br]If a function can be expressed as [math] f(x) = ax + b [/math] , Where [math] a [/math] and [math] b [/math] are constants, then the function is called linear function.[br][br]1. (b) What is the coordinates of vertex of [math] f(x) = ax^2 + bx +c, a\neq 0 [/math] [br][br]Solution: [br]The vertex of [math] f(x) = ax^2 +bx^2 + c [/math] is [br] [math] (h, k) = \left( -\frac{-b}{2a}, \frac{4ac-b^2 }{4a} \right) [/math] [br][br]1. (c) Identify the identity function: [math] f(x) = 5 [/math] and [math] f(x) = x [/math] [br][br]Solution: Identity function is [math] f(x) = x [/math] .[br][br]2. (a) Study the following graphs and identitify their nature as identity, constant, quadratic and cubic function.[br]Solution:[br][img]data:image/png;base64,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[/img][br]This is a graph of constant function.[br][img]data:image/png;base64,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[/img][br]This is a graph of identity function.[br][br][img]data:image/png;base64,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[/img][br]This is a graph of cubic function.[br][br][img]data:image/png;base64,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[/img][br]This is a graph of quadratic function.[br][br][img]data:image/png;base64,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[/img][br]This is a graph of cubic 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[/img][br]This is a graph of quadratic function.[br][br]3. (a) Draw the graph of [math] y = x+ 2 [/math] [br]Solution:[br]Given, [math] y = x + 2 [/math][br][math] \begin{tabular} {|c|c|c|c| } \hline x&1&2&3 \\ \hline y& 3 & 4 & 5 \\ \hline \end{tabular} [/math][br]Therefore, passing points are (1,3),(2,4) and (3,5).[br][img]data:image/png;base64,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[/img][br][br]3. (b) Draw the graph of [math] y = 6 [/math] [br]Solution:[br]Here [math] y = 6 [/math] represents the horizontal line passing through (0,6) .[br][img]data:image/png;base64,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[/img][br]3. (c) Draw the graph of [math] y = x^2 [/math] [br]Solution:[br]Given, [math] y = x^2 [/math] [br][math] \begin{tabular} {|c|c|c|c|c|c|c|c|c| } \hline [br]x&-3&-2&-1&0&1&2&3 \\ \hline [br]y& 9 & 4 & 1 & 0 & 1 & 4 & 9 \\ \hline \end{tabular} [/math] [br]Hence passing points are (-3,9), (-2,4), (-1,1), (0,0), (1,1), (2,4) and (3,9).[br][img]data:image/png;base64,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[/img][br]3. (d) Draw the graph of [math] y = -x^2 [/math] [br]Solution:[br]Given, [math] y = -x^2 [/math][br][math] \begin{tabular} {|c|c|c|c|c|c|c|c|c| } \hline [br]x&-3&-2&-1&0&1&2&3 \\ \hline [br]y& - 9 & - 4 & - 1 & 0 & - 1 & - 4 & - 9 \\ \hline \end{tabular} [/math][br]Hence, the passing points are (-3,-9), (-2,-4), (-1,-1), (0,0), (1,-1), (2,-4) and (3,-9).[br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAewAAAKFCAYAAAAOOdpvAAAgAElEQVR4Aey9DdAexXUmqopDuXa9G/8byjFer5fE3tgO8d1bvlwld8vlzb0ur8M1ZcIGGy8RKJGNV2tWFbiksHZh+TEKLAmsYiH/ycAqirBieWUQGEtGWKVYWOZHFghkVFrJFhYlpAiwwLIsoG+d96VH/fY7Z6Z7pk93T39PV331zvT09DnPc87M881MT88sFbjce++9gXtM0x1wpOGds1pKPDh8Q6svJR7AkVfmIR7N8ZjVvNl/Kwj350xyD8RDkl3Pvg8cUOrhhz13yrM58iqvuCAeMyMeEGwmzjgAGGISVRcRj//8n5X68IeVKuAuVBHxUBQK3BFMdEjXmkU8ammpKiHYFRWTC0icST5SrxURj/e9T6lZs5S6/PLUdPa2X0Q8INi98yB0B8irZkYh2Aw/SByGmETVRcTjTW8aC/Z/+S+JWAxntoh4QLDDJUSgnpBXzURCsBl+kDgMMYmqBx+PJ59U6ld+ZSzY8+cnYjGc2cHH42UqgCNcToToCfFoZhGCzfCDxGGISVQ9+HisWjUWa7ol/m//bSIWw5kdfDxepgI4wuVEiJ4Qj2YWIdgMP0gchphE1YOPB11Vk1jT32/9ViIWw5kdfDxepgI4wuVEiJ4Qj2YWIdgMP0gchphE1YOPxzvfeVyw/8k/UerYsURMhjE7+Hi8TANwhMmHUL0gHs1MQrAZfpA4DDGJqgcdD3p+/au/elyw6Sp74O9jDzoeRg4Dh0FGBouIR3MQINgMP0gchphE1YOOh/n8Wt8WX7w4EZNhzA46HgYFwGGQkcEi4tEcBAg2ww8ShyEmUfWg4/GpT01eXZNon312IibDmB10PAwKgMMgI4NFxKM5CBBshh8kDkNMoupBx+Pd754W7De8oZHJ7du3q1e84hVq1qxZ6tRTT1UvvvhibXuqp+3UjtrTfjHKoONhEAQcBhkZLCIezUGAYDP8IHEYYhJVDzYeNH+4vg1u/7Y8x164cOFIiEmMFy1aVMv8ddddV7W59NJLa9tIVA42HhYZwGERkngV8WgOAASb4QeJwxCTqHqw8fjbv+UF+6abGtk8evSoevvb3z4S5Fe96lVq165dE+337Nmj/tE/+kej7W9729vUkSNHJrZLrgw2HhYpwGERkngV8WgOAASb4QeJwxCTqHqw8TDfv7avsP/wD1vZXLduXXUF/WH6cIhRPvShD1Xb7r77bmOL/OJg42FRAxwWIYlXEY/mAECwGX6QOAwxiaoHG4+659dauE86yel97HPPPbcS5hUrVowisHLlyqruE5/4RPSoDDYeFlPAYRGSeBXxaA4ABJvhB4nDEJOoepDxqHv/Wou1/n3ssVZGDx48qN7whjeMBPqkk04a3RqnX3q2/drXvlbR9thlkPGoIQk4akhJWIV4NJMPwWb4QeIwxCSqHmQ86t6/1kKtfx3fx16+fHl1Ra3FmgT71ltvTRKRQcajhingqCElYRXi0Uw+BJvhB4nDEJOoepDxaHp+rQXb4Tm2pvz3f//3K9EmsX7/+9+vN0X/HWQ8algCjhpSElYhHs3kQ7AZfpA4DDGJqgcZD3P+cC3Q9q/jc2yinUaJk1Drv507dyaKhlKDjEcNW8BRQ0rCKsSjmXwINsMPEochJlH14OLh8vxai3fL+9gm5Vqs6TdlGVw8GLKAgyEmUTXi0Ux88KMehDcTHnsr4hGb8ZftuTy/1oLt+BybeoZgh40njo+wfPbtDfFoZhCCzfCDxGGISVQ9uHjUzR+uBdr+9ZhXHIIdNgEHl1cMfOBgiElULRUPCDYTUCnCGXNi1cAhRm1zx03vX9uC3TKvuGkIgm2y0X8Zx0d/DkP2gHg0swnBZvhB4jDEJKouIh6XXTaepvTyyzuzCMHuTF3tjkXklcIgwNrgJqyUyisINhNUKcIZc2LVwCFGrX/HEGx/zoT3wPEhTLBn94hHM2EQbIYfJA5DTKLqIuIRQLAT0T9ltoh44Mp0Kq6pK5BXzRGAYDP8IHEYYhJVFxEPCHai7OHNFpFX+MeDD3CiLVJ5BcFmAipFOGNOrBo4xKj17xiC7c+Z8B44PoQJ9uwe8WgmDILN8IPEYYhJVF1EPCDYibKHN1tEXuEKmw9woi1SeQXBZgIqRThjTqwaOMSo9e8Ygu3PmfAeOD6ECfbsHvFoJgyCzfCDxGGISVRdRDwg2ImyhzdbRF7hCpsPcKItUnkFwWYCKkU4Y06sGjjEqPXvGILtz5nwHjg+hAn27B7xaCYMgs3wg8RhiElUXUQ8INiJsoc3W0Re4QqbD3CiLVJ5BcFmAipFOGNOrBo4xKj17xiC7c+Z8B44PoQJ9uwe8WgmDILN8IPEYYhJVJ1lPO65R6lTT3VnBILtzlWkllnmVQfswNGBNMFdpOIBwWaCJkU4Y06sGjjEqFXqXe8azw3uagKC7cpUtHY4PqJR7WQI8WimCYLN8IPEYYhJVJ1tPOjLW64Fgu3KVLR22eaVJwPA4UmYcHOpeHicbdwQSjnqZj1cK+AIx2WInrKNBwQ7RHiT9ZFtXnkyAhyehAk3l4rHLOoYf+AAOeCfA6Nj/mXBduFvz5w5o1vou+fMwTGH8w5yADngnQO4wmb+06ITcAkFOISjiCtsYYJlu8fxIcuvb++IRzNjEGyGHyQOQ0yi6mzjAcFOlBFhzGabV57wgMOTMOHmUvGAYDOBkyKcMSdWDRxi1I47hmALEyzbPY4PWX59e0c8mhmDYDP8IHEYYhJVZxmPw4fHr3XRr0vBKHEXlqK2yTKvOjAAHB1IE9xFKh4QbCZoUoQz5sSqgUOM2rFY0xW261U2BFswGN26xvHRjTepvRCPZmYh2Aw/SByGmETVRcQDgp0oe3izReQV5hLnA5xoi1ReQbCZgEoRzpgTqwYOMWr9O4Zg+3MmvAeOD2GCPbtHPJoJg2Az/CBxGGISVRcRDwh2ouzhzRaRV7jC5gOcaItUXkGwmYBKEc6YE6sGDjFq/TuGYPtzJrwHjg9hgj27RzyaCYNgM/wgcRhiElUXEQ8IdqLs4c0WkVe4wuYDnGiLVF5BsJmAShHOmBOrBg4xav07hmD7cya8B44PYYI9u0c8mgmDYDP8IHEYYhJVFxEPCHai7OHNFpFXuMLmA5xoi1ReQbCZgEoRzpgTqwYOMWr9O4Zg+3MmvAeOD2GCPbtHPJoJg2Az/CBxGGISVRcRDwh2ouzhzRaRV7jC5gOcaItUXkGwmYBKEc6YE6sGDjFq/TuGYPtzJrwHjg9hgj27RzyaCYNgM/wgcRhiElUXEQ8IdqLs4c0WkVe4wuYDnGiLVF5BsJmAShHOmBOrBg4xav07hmD7cya8B44PYYI9u0c8mgmDYDP8IHEYYhJVFxEPCHai7OHNFpFXuMLmA5xoi1ReQbCZgEoRzpgTqwYOMWr9O4Zg+3MmvAeOD2GCPbtHPJoJg2Az/CBxGGISVRcRDwh2ouzhzRaRV7jC5gOcaItUXkGwmYBKEc6YE6sGDjFq/TuGYPtzJrwHjg9hgj27RzyaCYNgM/wgcRhiElUXEQ8IdqLs4c0WkVe4wuYDnGiLVF5BsJmAShHOmBOrBg4xav07hmD7cya8B44PYYI9u58p8XjooYfUrFmzRn//6l/9q1qW3vve9462v+IVr1APP/zwqA0Eu5YqpWZK4jDws6suIh4QbOSVEANFHB8z7E7BBRdcUIn2rbfeOpEZN954Y7XtwgsvrLZBsCsqJhdwAEzykXrNjMd3vqPUVVdNevT000otWaLUOecodcYZSp13nlJf+IJSVN+3uPZ95ZVKkW9sgWCz1KTaYOZVKh9C2AWOECyG68MlHgcPHlSvfe1rR8L85je/WR0+fHjkwL59+9SrX/3qUf1JJ52knn322coxCHZFxeSCC+GTe+S5VhqOPXuUOvNMpfbtm+T7M59R6vTTp/8++UmlXnppsq3vmmvfTzwx9o18rC0Q7FpaUlaWdnyk5DKE7ZkWj89//vPVlfSll146ovDjH/94VbdixYoJWkeC3fl++sv34OlevC4zjXCNO9ffkuJBwjt//vjK2eT7Bz8YC/X55yv1ox+Ntzz+uFLnnjuu37rVbO237Ns3XeWTwNcWCHYtLSkrSzo+UvIYyvZMjMd73vOekUCfcMIJ6gtf+EIl1h/4wAemaK2UttP9dAj2FKG5VZRyADz++ONq7dqxANtX14sXj+u/+91J9nX7r351st5nzbdvusqmK32yPVUg2FOUpK4o5fgAjtSZNGnfJx4bN26sRFoPRKOBZjt37pzsVClVCXaX++mvfOUrR4boVxcfR/U+Of4CR15ROXr0l4quoC++eNqvz352LJJ7905uo1vTJJ60vWvp0vdFF6mRr1O34iHYXcMgth+OczFqO3U8U+Nh3gYn0V64cGEtf5Vg01bf++l0yU6dz549u+p8phJeEZDZQinx0LemrUc6I7b/6I/GwvzCC5PkHzs2rqftXUuXvslH+keBfJ4oEOwJOnJYKeX4AI4csum4D77xuP/++6urbLo1fujQoeOdGUsTgk31PvfT582bNzJyLj0sfLn4Oqr3y+0XOPKKyI03MiKolProR8fb6jwm4aTtXUuXvrdsGftzww2WVQi2RUj6VRzn6WNgejBT49HpCpuI87mfbhKtl2cq4Rp/br+lxINeRSTxrXtNi+rpr65QPb3m1bV06Zt8pP2mBp9BsLuGQWy/Uo4P4BBLkU4d+8SD09zHHntsyvbUFTa1cFX7qd5m2Ivvdfhzq/NJnNx8N/2hV7k4Ue5yFWz23bTcpW96dk2+ks8TBYI9QUcOK6UcH8CRQzYd98EnHu9617uq2+HXXXddtfz+97//eIcvL9UKtuv99KneINh1lCSt80mcpI62GP/IR3jB5p4z0zNtEk6JZ9htfZPdqSt7CHZLlONvLuX4AI74udNk0TUeixcvrgR6zpw5oy7/5E/+pKqrfQ/bNowrbExNaudE6nV9hT018lopRTpIAmmPEtevWL08H0EnCF36xhV2J6qT7OR6Yk3inIdR4PAgK0JTl3iYb2bRjGe0TsWsb53pzOd+eh1uF0fr9sutDjjyisiCBWNRrhs8uXTpeNu6dZM+0zoJOb1L3bV06fuZZ8Z2jSmAx+Zxhd01DGL74TgXo7ZTxzMpHubcJzfddNMEX7Su38lunEvc5376hIWXV2YS4XX4c6srJR56AhMagW2XBx8cC+Qf//Hxmc5oxjM909nU61V2Bw3rXfrWo8Sn/lGAYDcwnWZTKccHcKTJH85qWzx++MMfVoJMX+WqK/prXSTc1J7KxDNs3/vpdUbaHK3bJ8c64MgrKjS9KF0tL19e7xfNGU7b7b+pq1x1vE19T9O1Pn3T3vThHfKDxH6iQLAn6MhhBcd5DlE47gPicZyLuqVKsM375q730+s6BOF1rKSrKyUev/jFLxQJ59SrUi9Tu3+/UvTeMw0wowFqH/uYUn/910rR7Wm7aFG367l1n76pD/LxT/+0pjcIdg0paatKOT6AI20e2dal4lEJdpf76baTtC7laJ0tyTrgkGTXv+8dO3Yo/Uya/RqWY7c0wnvqlSvHfdua7d49vrqu/cwmBLuNvujbcZxHp7zRIOLRSM/4lnjX++l1XYPwOlbS1ZUWD7rFTbOe9Snf/KZS11zTpwd+X7qqr7sNP9oDgs0Tl2hLacdHIhqDmUU8mqmsrrCbm7lvBeHuXMVoWVo89Pewn3yyO3v0QY+6W+XdexzvST7RlTt7BwCC3Zfi4PuXdnwEJyhyh4hHM+EQbIYfJA5DTKJqMx50u3nRokSONJj93OeUqr0VrveBYGsmsvk18yobpzo4AhwdSBPcRSoeYQSbLi1WrVJq/nz13D//54I0xOtaivB4CMaWgCM24/X2NmzYoK77v/9vdeWsWWrdueeqY/QpsQEX5FVewUM8BhKPd75TKZrR7G//VqkOtwm7CbYh0Ioc+NVfVWrWrON/eXHXyRscAJ1oE9tpqPHYvHmzetvb3qne+MZ3q1P+xWfUO/7FRerkN/7v6uSTT1G0bahlqPGw+QYOm5G068XHw9RJWj7lFKU+9amxgNtTNdaEwk2wDxyorqDVu989LdC2EzWGhlZVfOIMLCBDjAcJ8qte9Rr1u7+7bur98NmzN6hXv/qkwYr2EONRl/LAUcdKurri42Frpb1OF8Ak4P/jf9RegdcLtnkFTQJtd9q2ni7ewSwXnzjBmIrT0RDjQVfWdWKt3wMn0aYr7cOHD8chMaCVIcajDj5w1LGSrq74eLRpp73duoU+FmxToOtucdudtK2ni3cwy8UnTjCm4nQ0tHjQM+sTT/ydqStrLdb69+STf0/dfvvtcUgMaGVo8eCgAwfHTJr64uPRpp0t22epN71JqV/5Ff+r6KaOaTTswP/20MCAgWMg/4Ejbi5u++wF6paLz1D/1+/9M/X2t//HVsH+jd+4WP0fs9+ill70B+qBS+cNJueQV3Hzqu1chHgMJB5NuumwbZb37W6HTtGnMQAPfIX9ZzBDPnf+2ix17W/PUqf/P8f//uVvzFJvf/v8VsE+5ZSL1DtPOb4f9XHZ/zZLbX8NcgjnEeQAcmAyB2apyy8fT378B3+gRgPKfu3X+p9gqc+B/+2mK+yBYyD/gUMuF+/883PU6f/xHbV/sz96snrNa36zVbDf8IbfUe87/ddr+6C+1/z5x7LMQ+SVXF51Oe8gHgOJR88LjvpBZ489phR9n/MTn1DqpJP8BTzN44+gVot/lhKULfnOcorHhh0b1OmLT6/9u/Zb16otu7eoF158YfQ6l+ugs21PbFNL711a2yfZuvuRu+VJ9rCQUzw83J5qChxTlCStKD4evoL9hjco9Yd/qBR9q/fhhyc/r8lGigT8q19V6uyz3QSc7Wg4G4pPnOGEYuRpDvHY98w+dc6Xz5kS1QtXXqi27t06xSi91vX6179FnXZa/WtdJ55Y/y42iTf1WfdPwd5De6fspKjIIR4hcANHCBbD9VF8PNoEmy6QDYG2ma2/wrZb2es7d46vwEnA3/KW6Stwu/0A14tPnIHFJHU8rv/29VMCOu/WeWr/z/Y3MkmiTa9u0Yhx34lTDhw+oBbctmDK7tVrrx5dwTcaFt6YOh6h4AFHKCbD9FN8PGzBNgWaLoxbZkDsJth2bIxb6Edf9zp76yDXi0+cgUUlVTyO/PLIlGDSle+OJ3c4M3jkyBG1bt06dc2/+TejqUlv//jHvd693rl/Z60Pz/78WWcfQjdMFQ/gqGcA8ajnJVUtGw/rFnebQNv+hxFso1fWUaPNEBaBI68opYjHpp2bpoTylu/d0p2Ynh//WLll5ZQ/6x9d392fHnumiEcPd9ldgYOlJskGxKOZdgg2ww8ShyEmUXXseCzZsGRKHHtf0fYUbKK+7or/hvU3RI9K7HhIAQQOKWa79Yt4NPMGwWb4QeIwxCSqjhmPs5aeNSHWl66+NMwz4wCCrem/4vYrJnyk2/Q0Mj1WGeJ0qnXcvPTSS3XVg6srBcff//3fD477mA7LC/ZTT6nRbGoxUQWwVQkE+U/zSJ5wwvjvrrsC9B6viwrHoUNKffCDYwynnabUT34Sz4kAlioc1Nc99yh16qkBep3s4uixo1MiuPHxjZON9NratWMuaRAJ5YZLXgQUbHKj7pY9YRAvQvyL+20aGPjxUEEZ+PmpwvHywkv79w9SLyZwXH/98YHYdK4NWOQFm0SCTmoDK5VAXHXVcXGjkzKdnAdUKhw0CcwPfzj2nN6xnz17QCiUqnCQ1+96V/CcqhNrer2KLaZIu+ZFYMEm32jwm/36l7hoC/DP8iy14eXjYXRlOsDjoaLl5fPTCIdrHlY7Z7gwUL2YYPLtb1fq/vsnqkKtBFfSiRMrvex93XXBT66hwDf1U+F48cXjzY4eVeo97zm+PoClCsfy5ce9pVcHhvqPh0YR8J/AOrFue11r6p9QF38EBJvoOPT8ofii7YJXxyrH35ePh+9+97vjV2kGdjxUlL58fnrggQeUGuD5qcJBCwPWiwoH/dP0gQ+oF16QeTwlJ9jbt49nSiMkAzy4K6HTkXjoIaUWLlRq3z5dM4jfKRzkNR3kAreUJQmZwhEop+i5r32F+twvnmuHYtu31+t6EBJsMlU3GE30StsFbx0HmdWN8mqAx8MUjQM9P1U4Bq4XFY4PfECpV7xiJNoSV9nBBXv0Hyv9p0eTqjz//BjHAA/uCYFYuXL8T8db36rURuaZZhWxvBYmcGjXNm0aT3yj1wfwO4UjUE7ZYu0scrZ9e72OU0HBJnN1dwrEBqK54K3jILO6h0joBng8TNA44PPTCEcBejERj2PH1Et/8zdKvfa14/E2Exv7rXQXbDpg6/7IH3qusmfPcc9yPrjrMHD+0u2OV77yOK6clnxw0GOKXIsrDi5GHrjOvOnMiatrZ7EmG7Z9e73OD2HBJpPRRNsFbx0HmdXt3bt3/NguM786uZPz+akJ0JD0ogmHsW3Xrl2jub/p9njI0l2wm7ygg7nur2mfzLZNXdFp/wZ2oprCQQPPnnhCoxnM7xSOnnGwp/z0fsfatm+v1zEbQbDJLN3SN+8czF8xv86bfnUuePtZiLL3jq99bZDHg01OdXwMMS7kc92fDXJA61U8zjwzqNfBBbty1HRzgElUi4MwDQzLBI6DB5WieeAHWCZw9IzDsk3LJgTNW6zr7LvkRSTBJvds0aaJYIIWF7xBDQp0dvCgevSb3xToOH6X1fFRQlwKwLBRPzp93/uCJgMEm6GzOgDM7QN8baLCcfiwUj/60RjNww8rRd/7HlCpcJDPhIUOavr1LPZrUDRPd6eSyWtdTb7vemrXxD8m23+6vam5+7Ye/LsbEW458OOhlp0Bnp9qcQxZsF9+neuXP/uZUvPmKfWNb9RC7FoJwWaYqwSC/kOiBKI/OknThBkDKhUO/X6jxnL++QNCYb2HrTHQr0exX39iJ0Vx6VOfHH3yIuIVtoawedfmCdGmL4D1Lh357203ZAcDPx4qKgZ+fqpwmAuex7W5a/Ll979fqTe/Wb3027+tFD1uCVz8zngOxiuBcGibcxPgyCs6feNhv74V/BaxC10JBJvcsh8BeA2uc8GFNmAgEAN9j/NAbvTuRmrqXgg2E5pSEgc4xgE25wen0eFJSiLBJqyh8SOvkmQQaxTxYKlJskEqHhBsJpxShDPmxKqBQ6m7H7l74rZwsivMhIJt32G4Y9sdvXIOedWLvuA7Ix7BKe3VoVQ8INhMWKQIZ8yJVc90HDTFqPmKU5BnuF2jlVCwyWX7Gf6+Z7rP2jfT86prCkjth3hIMdutX6l4QLCZeEgRzpgTq57JOOyrShqAlbQkFmzCvmX3lol/YLrebZjJeZU0hxjjiAdDTKJqqXhAsJmAShHOmBOrnsk4LltzWSVOFyy/QIxj544zEGzy1Zw05pKvX+LsvtlwJueVyUMuy4hHLpEY+yEVDwg2E2cpwhlzYtUzFYf9DnLXK8mggclEsO07D8SVb5mpeeXLU6z2iEcspt3sSMUDgs3wL0U4Y06seibisL9ctffQXjF+vTrORLDJZ+LEfLZPnPmUmZhXPvzEbot4xGa82Z5UPCDYDO9ShDPmxKpnIg66/a3FaMX3V4hx691xRoJNvq+6f1XF09yb53rBmYl55UVQ5MaIR2TCW8xJxQOCzRAvRThjTqx6puGwb4XT7d9sSmaCTbzof2zo1+fW+EzLq2xyiHEE8WCISVQtFQ8INhNQKcIZc2LVMwkHPac2BajPa0siAclQsO3X3lyf9c+kvBLJhcCdIh6BCe3ZnVQ8INhMYKQIZ8yJVc8kHNd+69pKsJfft1yM084dZyjYhMW8Nb7orkVO8GZSXjkRkrgR4pE4AJZ5qXhAsC2i9aoU4br/WL8zBUfWt8J1sDMVbHLPvDNBXzRrKzMlr9p4yGU74pFLJMZ+SMUDgs3EWYpwxpxY9UzBYQrOnoN7xPjs1XHGgu17a3ym5FWveEfcGfGISLaDKal4QLAZ8qUIZ8yJVc8EHHc+fGd1hXjRqovEuOzdccaCTdguXX1pxeOarWsa4c6EvGokILONiEdeAZGKBwSbibMU4Yw5serScTz782crkaGr7KRzhbdFMXPBtt9fbxq0V3petYUyt+2IR14RkYoHBJuJsxThjDmx6tJx0BW1vh3e9wtUYkHQHWcu2OTmhh0bKj4vXHmh9nzqt/S8mgKceQXikVeApOIBwWbiLEU4Y06sumQc9kAz11eSxMhu63gAgk0Q9D9A9LvtiW21qErOq1rAmVciHnkFSCoeEGwmzlKEM+bEqkvG4SIsYsR26Xgggu3yj1DJedUltKn3QTxSR2DSvlQ8INiTPFdrUoRXBiItlIpj085N1ZVg063bSDS7mRmIYBMY81HD+kfXT+Hrmlff+Y5SV1011V1V8Td/o9Tpp1er4gsaR5PdK69UivzOuWgcOfvo4htwNLMEwWb4KSVx9uzJ9BUnhneu2oyH/bWppsFRXH9J6gck2PZgPlo3ixkPs75pmVLxzDOV2revvtWjjyr1kY/EFeydO3eqNrtPPDH2O+dDqUs86qOQthY4mvmHYDP85JQ4bVclDIRRddOVQ9N+fbc12e1yxWLGgwaX6dvhWX3co420AQk2QTFnQFv94OoJdGY8JjYwKy+9pNT8+Up94Qv1DbZtU+qP/mgs1jGvsF3tLlmi1Gc+U+97DrW+8cjB5zofgKOOleN1EOzjXEws5ZI4bVclE05bK21XDlbzYKttdrtcseh4PPeL5yqxJtG2r/yCgZDoaGCCbd/JOPT8oYoVHY+qomVh7dqxGNddXd966/jK+s//PK5g+9ilnKV/JAhHjsU3HjliIJ+AozkyEGyGnxwSp+2qhHF9VO165dDUR5dtrnZ9r1h0PL608UuVYNc9W+3ic7R9BibYxIs5VmDJhiUVVToeVUXDAuXx+ecrdfHF9Y1ICP/6r5U6diyuYER2jvoAACAASURBVPvaveiiMQ7Ck1vxiUduvpv+AIfJxvQyBHuak1FNDonTdFXCuD2q9rlyaOrHd5uPXd8rFooHTYqib4XTb/avcdkEDlCwCYLJuR4v4HN8/OAHYyFewXya/LHHjhNFIkp/MQrZPXDgwMiUi13yn9oRntyKTzxy8930BzhMNqaXIdjTnIxqUidO21UJ4/aomk4qpVyxbNiwQV133XVq7ty56tPXflr9wY1/MBKQLbu3NFGQ57aBCja9i61F+5PXfrKKx7p169QxuixuKTfe6C50LsLZYs5rsz7OXexu2TLGccMNXiaiNNY4ohgTNAIczeRCsBl+UidO21UJ4/aoOuUVi/bL5QTYdMWyefNm9ba3vVO98Y3vVqec8p/Ub/7mJep1b3qvetXrXqd+789+T5sZ1u9ABZtIJs7/yRveoP7pa06p4nHyyb+nTj75FEWxaioXXjgWuqefbmo13uaSN+29uLfQx7mLXfKf2uU4+EzjcEeeZ0vgaI4LBJvhJ3Xi+FyVMBBG1S4noqb9u25zsctdsZAAvOpVr1G/+7vrRidI3Rf9zp69Qf3TX3tTq0h09dtrv3vuUerUU913GahgUzz+8T9+tTrt/7y7Nh6vfvVJjfGgV7kodi5Fx9qlbYg2+jh3sUt3vagd4cmtaBy5+eXrD3A0MwbBZvhJnTg+VyUMhFG1y4moaf+u21zsclcsdGVdJ9a6TxJturI7fPhwV/fC7Peudyk1y+MQGqhg942Hz7vVOsZ9A6T7sX/tfvVxrtvZ2+11anfGGXZt+nWNI70n/TwAjmb+PM42zR3prSBcM9Hv1+eqpMmS64moqY8u21zs1l2x0DPrE0/8nakrOd2f/qXbsbfffnsX18LuU7hgh4iHzmWKd1vR8W1r17Zd92P/2vvp85VuZ2831+vy1dyeclnjSOlDCNvA0cwiBJvhJ3XicFcl+sRi/zIwKuHjtrvW2/b0Ord/23a9H7Uzr1iuueaa0TNSvT/3+453/Lm6kmZgSV0KF+wQ8ViwYHwr+dDx17jZqOl4sw0Cb9DHuYvdZ54Z46C7X7kVjSM3v3z9AY5mxmYRQfjLi4MXX3xx9JyMTiL0X72OD4VSn1jsX9qm2+lfs33ddt2u7dfsJ6Rd84qFMJMf8+bNU6ecciGLU9unQWg0crzN967bCXNdMfsbbX9ZsM16bnnPnDmjW+i758wR85uz3bW+bzz27dunFi8e5y2NWXj44YdZ7MSnji8t1/msY1K3rWudi13yW4+5IDyEq6s97JfX+XZI8cAVtj4DWL8UxJTF56qkyU/zBNjULvQ2F7t1VywhbsEGwUJCXPdnd174FXaIeGzdOhbi5ctt8qbX2/Kmbft0j801+jh36ZfmGaB2Dz7Y3GeKrRpHCtshbQJHM5sQbIaf1IljXpUwLjpVu5yInDrybORi17xiMbvvO8jJ7Et8uXDBJv5CxOOTn3R7Haotb9q2+8ZbH+cu/dLrXH/6p74W4rTXOOJYk7MCHM3cQrAZflInjs9VCQNhVN12Imrb3tR30zaXfrkrFnqN6LWv+3V12mn1r3WdeGL7u79NvgXdNgMEm+Lx+te/hY3HG9/49sbXuojvdevGV6d9v3j1wgthX6tyPc537x77n+tnNl1xBM19gc6Ao5lUCDbDTw6J43pVwkAYVbcJZ9v2pr6btrn023TF8pkbPzOaJOXXXvdO74k6mvwKuo1eKyPBdn29bKCvdRFnJNr0Kh2N4Lcnsvn0X33aiVYarEXzC/Qp3/ymUtdc06eHyX1dj3OaOTDHwWYajSsO3T7XX+BojgwEm+Enh8QJdVXCQBxVh75iabJlbmu6YqGvQtFUmB/+yw+r0+afpmikMg0wo9e4kr97bYIgsdZ/Zj23PGDBJkhHjhxRNB2pjsfsT89WH/pvHxrFSs8xzkGnev3luSefbGrVvO2zn1WKxj6EKi7HOflLr6b1vTsQyue6flxw1O2XWx1wNEcEgs3wk0vi9L0qacMR+oqFoXOquumKZfl9y6u5qx/48QOjfdtwTBnIsWLggm1SSvEw5xi/5Xu3mJvZZbqlvGgRuzn6Bpe8+tznlMr1VrgmzAWHbpvzL3A0RweCzfCTS+L0vSppwxH6ioWhc6K66YrlyC+PVGJNV9m6tOHQ7bL+LUywiWv9URD6Nb+XnXUcDOeKyCt8R9qIaB6LUnkFwWbiK0U4Y66xus9VSU44NMimK5Y1W9dUIrBhxwa9y+id12plqAsFCjZ9NU2L9qr7Vw0uMjkeH11IBI4urMntIxUPCDYTMynCGXNi1UPCYV9dm9+7HhIONpgFCjZh1YJNv2bMWB4y2lBEXuEKO6OMGrsilVcQbCbUUoQz5sSqh4Rj4+Mbq5P/3Y/cPcHJkHBMOG6uFCrY6x9dz8bNhJ/jchF5BcHOLrWk8gqCzYRainDGnFj1kHCYV2p0tW2WIeEw/Z5YLlSw6arajN0LL74wATvnlSLyCoKdXYpJ5RUEmwm1FOGMObHqoeDY/tPt1Ul/2aZlU3wMBceU42ZFoYJNEFc/uLqKnx7Zb0LPdbmIvIJgZ5deUnkFwWZCLUU4Y06seig4Llh+QXXCr3undyg4GgNZsGCb4w/m3TqvkYacNhaRVxDsnFJq5ItUXkGwmVBLEc6YE6seAo69h/ZWYr1kw5JaLoaAo9Zxs7JgwSaYS+9dWsVx11O7TOTZLheRVxDs7PJLKq8g2EyopQhnzIlVDwEHTbqhn4Hu3L+zlosh4Kh13KwsXLD3HNxTxfFLG79kIs92uYi8gmBnl19SeQXBZkItRThjTqw6dxzP/eK56iR/7lfOZXnIHQfruLmhcMEmqHNvnlvF88DhAyb6LJeLyCsIdna5JZVXEGwm1FKEM+bEqnPHcce2O6oT/OZdm1kecsfBOm5umAGCbU5XSpPg5F6KyCsIdnZpJpVXEGwm1FKEM+bEqnPGQa//6Fvh9Ns06UbOOJyDNwMEm7gwY2q/nufMVaSGReQVBDtStribkcorCDYTAynCGXNi1TnjMK/G7IlSbEJyxmH7yq7PEME2J1JpumvC8hRxQxF5BcGOmDFupqTyCoLN8C9FOGNOrDpnHD7PO3PG4Ry8GSLYruMSnHkTbFhEXkGwBTOkW9dSeQXBZuIhRThjTqw6Vxzmq1wuI4pzxeEVuBki2MSJy8h/L+6EGheRVxBsoezo3q1UXkGwmZhIEc6YE6vOFceK76+onnVyr3KZpOSKw/SxdXkGCbb5D5nrt7Jb+RNoUEReQbAFMqNfl1J5BcFm4iJFOGNOrDpHHOasWOd8+Rwn7DnicHLcbDSDBJtg02t6egAa3SbPsRSRVxDs7FJLKq8g2EyopQhnzIlV54iDBiLpE7nroKQccXgHbYYJ9ta9W6s4tw0q9OYy0A5F5BUEO1A2hOtGKq8g2EyMpAhnzIlV54hDizX9ur72kyMO76DNMMG2X9vz5ivCDkXkFQQ7Qqb4mZDKKwg2EwcpwhlzYtW54aA5prVg03Ns15IbDle/J9rNMMEm7KvuX1XFm77IllspIq8g2LmllZLKKwg2E2opwhlzYtW54aAR4VqwaWCSa8kNh6vfE+1moGDT9KQ63vRxkNxKEXkFwc4trSDYsSOCAzk84+Zgs0u+fomXgSLiMQMFm4J86epLK9HObX7xIvIKgu11LonRWCqvcIXNRE+KcMacWHVOODbs2FCduF0Hm2licsKhffL+naGCbc5oR7Og5VSKyCsIdk4pNfJFKq8g2EyopQhnzIlV54RD3xqlX9fBZpqYnHBon7x/Z6hg5zz4rIi8gmB7H4rSO0jlFQSbiZwU4Yw5sepccJjfSvYZbKaJyQWH9qfT7wwVbOLKHHzmMlFOJ3477FREXkGwO0RedhepvIJgM3GTIpwxJ1adCw5zZjOfwWaamFxwaH86/c5gwTYHn+U081kReQXB7nQ4Su4klVcQbCZqUoQz5sSqc8BBn83Ut8MX3LagE9YccHRy3NxpBgs20bDwGwurPMhl5rMi8gqCbR5lWSxL5RUEmwmvFOGMObHqHHCYM5ttfHxjJ6w54OjkuLnTDBfsTTs3VYLdNQ9MOkMsF5FXEOwQqRC0D6m8gmAzYZIinDEnVp0DjhBXVjng6B2kGS7Y5p0W39f6enPPdFBEXkGwmeimq5bKKwg2E1MpwhlzYtWpcRx6/lB1VdVn4ozUOIIEaIYLNnHYdeKcIPzXdFJEXkGwayKbtkoqryDYTFylCGfMiVWnxnHHtjsqwd7x5I7OOFPj6Oy4uSMEW5lT067ZusZkJ8lyEXkFwU6SO01GpfIKgs2wLkU4Y06sOjUOPdiMfvuU1Dj6+F7tC8EeUWHmBL2jnbIUkVcQ7JQpVGtbKq8g2LV0K7G5YBlzYtVSiePisHk1tXLLSpdd2DYpcbBO+W6AYI8Yu/PhO6u7Lqk/CFJEXkGwfY9E8fZSeQXBZkInRThjTqw6JQ5631ZfTe3/2f5eGFPi6OW4uTMEe8TGsz9/tsqLZZuWmQxFXy4iryDY0fOmzaBUXkGwGealCGfMiVWnwmF+6OPqtVf3xpcKR2/HzQ4g2BUb137r2kq0U76TXUReQbCrvMplQSqvINhMhKUIZ8yJVafC8cCPH6hOyL4f+qgjIxWOOl8610GwK+rMD4LQR2FSlSLyCoKdKn1Yu1J5BcFmKJcinDEnVp0KR+grqFQ4ggYGgl3RaX4Q5LI1l1X1sReKyCsIduy0abUnlVcQbIZ6KcIZc2LVKXCYzygX37M4CLYUOII4bnYCwTbZUMvvW17dhek7xmGiY4+VIvIKgu0R8ThNpfIKgs3ET4pwxpxYdQoc5nevt+7dGgRbChxBHDc7gWCbbCjzC253P3L3xLZYK0XkFQQ7Vro425HKKwg2EwIpwhlzYtUpcMy9eW515RTqPdsUOBqDcuiQUh/8oFInnKDUaacp9ZOfNDYfbYRgT3Gk3yI458vnTG2LUZFdXnUEDRwdiRPaTSoeEGwmYFKEM+bEqmPjMD+jSN9ADlVi42j1+/LLlfrhD8fNbrpJqdmzW3dREOwpjlY/uLr6567LZ1enOvSsyC6vPP3XzYFDM5HHr1Q8INhMfKUIZ8yJVcfGYU5FGvIEHBtHa0CWLz/e5Nix8ZX28Zr6JQj2FC/mP3gppirNLq+mGHKrAA43nmK1kooHBJuJoBThjDmx6tg49C3Os794dlBMsXF4Of/ii0qdemr7LhDsWo7O++p51VV2qEcotYZqKrPOqxp/uSrg4JhJUy8Vj1nUMf7AQYgcuG3tbWr25bNHf3+x4i8GnVfcYW7z9NBDD6ln1q5Vv/zv/109/vjjjZj3zJmj1KxZavecOY3tbBulr//lyr+s8ubm/3kzuME5GTnA5ACusJkzM50kSygxcdB84foKO/RrOjFxjOI+a9ZIXElgJ/7qkuK66+pqp+twhT3NiVLKfA2QXvWKWaLnlRA44BAitmO3UvGAYDMBkSKcMSdWHROHFusFty0IjicmDi/naeDZE0+47QLBZnm65OuXVP/sHT12lG0XekO2eeUJFDg8CRNuLhUPCDYTOCnCGXNi1bFw0LeutWBvfHxjcDyxcHg5fvCgUjt3uu8CwWa5oulrdf6EenefNWZsyDKvDP9cF4HDlak47aTiAcFm4idFOGNOrDoWDvPLXDTyN3SJhcPZ78OHlfrRj8bNH35YKXo+3VYg2CxD9AEQLdgxv+CVXV6xDDVvAI5mfmJvlYoHBJuJpBThjDmx6hg4zHmhQ3yZq46MGDjq7LJ1NGmK+Xz7/PPZptUGCHZFRd2COf88fe0tRskurzqCBo6OxAntJhUPCDYTMCnCGXNi1TFwbP/p9urqKMSXuerIiIGjzm7QOgh2I53mF9627N7S2DbUxiLyClOThkqHYP1I5RUEmwmRFOGMObHqGDi+tPFLlWBLfds4Bg6xIOiOIdiaidpf8xvqSzYsqW0TurKIvIJgh06L3v1J5RUEmwmNFOGMObFqaRzm7fAb1t8wWBxijpsdQ7BNNmqXSaj1s+wYt8Wlj49akAKVwCFAao8upeIBwWaCIkU4Y06sWhqHeTtc8jamNA6xAJgdQ7BNNmqXY+WTNl5EXuEKW4czm1+pvIJgMyGWIpwxJ1YtjcO8HS55RSSNQywAZscQbJON2mXzjk2M2+JF5BUEuzaXUlZK5RUEm4mqFOGMObFqSRwxT66SOMTItzuGYNuM1K7H+ieQjBeRV8BRm0cpK6XyCoLNRFWKcMacWLUkjpi3LyVxiJFvdwzBthmpXUde1dLSWFnE8YF/PBpjTBsh2AxFOAAYYoxqXAkZZLgsQrBdWFK4c+NE00QjnK8m6Ei+IhUPCDYTWinCGXNi1VI4aL5nPZoXzxodwwfBdiRKKfOfQalXBckZqePDGWighsARiMhA3UjFA4LNBEiKcMacWLUUjg07NlSCLTVZikmKFA7ThvgyBNuZ4m1PbKvy645tdzjv59uwiLzCPx6+YRdvL5VXEGwmdFKEM+bEqqVwmNNISswdbhMihcO2I7oOwXam1/zkptR0t+RMEXkFHM55FauhVF5BsJkIShHOmBOrlsBhzkhFn0WMUSRwxPB7wgYEe4KOtpWF31hYXWWTgEuUIvIKgi2RGr36lMorCDYTFinCGXNi1RI41j+6vjqRrtm6Rsx3s2MJHGb/UZYh2F403/nwneJ5VkReQbC98ipGY6m8gmAz0ZMinDEnVi2Bw7wdvvfQXjHfzY4lcJj9R1mGYHvRTLmlBzYuumuR176ujYvIKwi2a7ijtZPKKwg2E0IpwhlzYtWhcZi3wxfctkDMb7vj0Djs/qOsQ7C9aaZHLlq0JUaLF5FXEGzvvJLeQSqvINhM5KQIZ8yJVYfGYY4OX7llpZjfdsehcdj9R1mHYHvTTI9ctGBLjBYvIq8g2N55Jb2DVF5BsJnISRHOmBOrDo1j8T2LqxPojid3iPltdxwah91/lHUItjfNO/fvrPLt+m9f771/2w5F5BUEuy3M0bdL5RUEmwmlFOGMObHq0Dj01c6FKy8U87mu49A46myI10GwO1F80aqLKtGmCXtCliLyCoIdMiWC9CWVVxBsJjxShDPmxKpD4njgxw9UJ87l9y0X87mu45A46vqPUgfB7kQzPXrR/yjSGwohSxF5BcEOmRJB+pLKKwg2Ex4pwhlzYtUhcax+cHV14qSZqGKWkDhi+j1hC4I9QYfrCj160YK9bNMy192c2hWRVxBsp1jHbCSVVxBsJopShDPmxKpD4jjny+eMTpxnfP4MMX+5jkPi4GyI10OwO1M89+a5lWjTx0FClSLyCoIdKh2C9SOVVxBsJkRShDPmxKpD4TA/ebj03qVi/nIdh8LB9R+lHoLdmWbztnjIueuLyCsIdue8ktpRKq8g2EzEpAhnzIlVh8IhdcJ0BR4Kh6s9kXYQ7M60mh8DCTl+ooi8gmB3ziupHaXyCoLNREyKcMacWHUoHDQqXD9HDHlL0hV4KByu9kTaQbB70arz74LlF/Tqx9y5iLyCYJshzWJZKq8g2Ex4pQhnzIlVh8Cx66ldlVjTe9gpSggcKfyesAnBnqDDd4W+u65Fmx7RhChF5BUEO0QqBO1DKq8g2EyYpAhnzIlVh8BhfoTh7kfuFvO1qeMQOJr6j7INgt2L5k07N1WCHeqjM0XkFQS7V15J7CyVVxBsJlpShDPmxKpD4DA/cygxn7ML+BA4XOyItoFg96KXJk3RV9ihPutaRF5BsHvllcTOUnkFwWaiJUU4Y06sui+OQ88fqk6SV6+9WszPto774mjrP8p2CHZvms0vxe3/2f7e/RWRVxDs3nkQugOpvIJgM5GSIpwxJ1bdF4f5sY9QtyG7gO2Lo4vN4PtAsHtTan6LPcTHQIrIKwh277wK3YFUXkGwmUhJEc6YE6vui8O8otn3zD4xP9s67oujrf8o2yHYvWk+cPhAdccnxDeyi8grCHbvvArdgVReQbCZSEkRzpgTq+6Dg17fCv3MsCvQPji62gy+HwQ7CKXmmAr6PnufUkReQbD7pIDIvlJ5BcFmwiVFOGNOrLoPDppRSgv2qvtXifno0nEfHC79R2kDwQ5Cs/mN7L5vLRSRVxDsIHkVshOpvIJgM1GSIpwxJ1bdB8eXNn6pEuxQ7712BdoHR1ebwfeDYAeh1PxGNr2b3acUkVcQ7D4pILKvVF5BsJlwSRHOmBOr7oNDf+xj3q3zxPxz7bgPDlcb4u0g2MEoptnO6O7PWUvPUn1m3isiryDYwfIqVEdSeQXBZiIkRThjTqy6Kw7zk4Z0pZ26dMWR2u8J+xDsCTr6rNzyvVuquz/0nfaupYi8gmB3Db/YflJ5BcFmQiZFOGNOrLorDvPb1xsf3yjmn2vHXXG49h+lHQQ7GM1bdm+pBJs+TNO1FJFXEOyu4RfbTyqvINhMyKQIZ8yJVXfFYY7EpRmmUpeuOFL7PWEfgj1BR5+VUG8wFJFXEOw+qSSyr1ReQbCZcEkRzpgTq+6CI/S7riHAdcERwm7QPiDYQekMMUdAEXkFwQ6aVyE6k8orCDYTHSnCGXNi1V1wmLOb0Yc/cihdcOTg94QPEOwJOvqumHnaddazIvIKgt03lYLvL5VXEGwmVFKEM+bEqrvguP7b11fPB1PObmaS0gWHuX8WyxDsoGEw7wTR1XaXUkReQbC7hF50H6m8gmAzYZMinDEnVt0Fh54sZcFtC8T88u24Cw5fG17tn3pKqdNPV+qEE8Z/d93VvjsEu50jzxb01S6dr11e78ourzzx6+bAoZnI41cqHhBsJr5ShDPmxKp9cdArMvoE2Gf0bWhAvjhC25/q76qrlPrJT8bVJNYk3G0Fgt3GkPf2vm8zZJdX3gyMdwCOjsQJ7SYVDwg2EzApwhlzYtW+OEiktWBv3btVzC/fjn1x+Pbv3f7FF4/vcvSoUu95z/F1bgmCzTHTud6cL2D5fcu9+8kur7wRjHcAjo7ECe0mFQ8INhMwKcIZc2LVvjguWnXRSLDPvOnMXjNIhQbkiyO0fba/hx5SauFCpfY5fMkMgs3S2GcDzXZG/2ReuPJC726yzStPJMDhSZhwc6l4zKKO8QcOKAduW3ubmn357NHfhV+8cEbnBXc862Nl+/btSq1cqdSsWUq99a1KbdyoHnrooUbO9syZM2q/e86cxnbaBn7djssFX1xQ5S3lMHhz4w08DY8nXGEzZ2ZK5hKKDw768pG+HZ7L61w6Bj449D69fkmI6/7qOqVn2K98Zd2WyTpcYU/yEWjNfL2LvuTlU6LnlY9zHm2Bw4OsCE2l4gHBZoInRThjTqzaB4c5EcWzP39WzKcuHfvg6NJ/731I3NsKBLuNoU7bn/vFc9U/mlevvdqrj+zzyhENcDgSFamZVDwczjJ+CKUc9fOif+uZhiPUVI/9ma/vIft4QLDrAxeptutUutnnlSN/wOFIVKRmUvGAYDMBlCKcMSdW7Yoj1McUpIC44pCy39gvXutqpCfGRvP1LrpF7lqyzitXEJg4xYOpOE2l8gqCzcRPinDGnFi1Kw7zda5tT2wT86drx644uvbvvd/73nf8GTe9g712bXsXuCXezlHHFubrXcs2LXPuJbu8cvZ8siFwTPKRek0qHhBsJrJShDPmxKpdcdCzPxpwdsbnzxDzpU/Hrjj62BDfF4ItSvHcm+eOcthnhr4i8gpX2KJ51aVzqbyCYDPRkCKcMSdW7YLDHLSz9N6lYr706dgFR5/+o+wLwRalma6s9VsOh54/5GSriLyCYDvFOmYjqbyCYDNRlCKcMSdW7YLDfC3G5/mfmNM1HbvgqNktryoItmg8Nu3cVAm269e7isgrCLZoXnXpXCqvINhMNKQIZ8yJVbvgML/O5XplIuYw07ELDmbXfKoh2KKxMO8UuX69q4i8gmCL5lWXzqXyCoLNREOKcMacWLULDn0b0efZn5jDTMcuOJhd86mGYIvHwvfrXUXkFQRbPK98DUjlFQSbiYQU4Yw5seo2HPSBDy3YK76/QsyPvh234ejbf5T9IdjiNK+6f1WVz3SLvK0UkVcQ7LYwR98ulVcQbCaUUoQz5sSq23CYJ7jNuzaL+dG34zYcffuPsj8EW5xm339Ai8grCLZ4XvkakMorCDYTCSnCGXNi1W04Ll19aXVFQrOd5VracOTq94RfEOwJOqRW9B0j+vJcWykiryDYbWGOvl0qryDYTCilCGfMiVU34TAH6fjOwSzmMNNxEw5ml/yqIdhRYuIziLKIvIJgR8krHyNSeQXBZqIgRThjTqy6CcfGxzdWV9eur8GIOdrScROOll3z2QzBjhKL9Y+ur/K67atzReQVBDtKXvkYkcorCDYTBSnCGXNi1U04vrTxS9WJbddTu8R8CNFxE44Q/UfpA4IdheY9B/dUeb34nsWNNovIKwh2Y4xTbJTKKwg2E00pwhlzYtVNOOavmD86sc27dZ6Y/VAdN+EIZUO8Hwi2OMXagGtuF5FXEGwd9mx+pfIKgs2EWIpwxpxYNYeDrqj14JxcpyM1SeFwmG2yX4ZgRwuROU3pzv07WbtF5BUEm41vqg1SeQXBZiIqRThjTqyaw2E+56Pl3AuHI3e/J/yDYE/QIblCryjqf0jXbF3DmioiryDYbHxTbZDKKwg2E1EpwhlzYtUcDnMk7bM/f1bMfqiOORyh+o/SDwQ7Cs1k5Oixo5VgL7prEWu3iLyCYLPxTbVBKq8g2ExEpQhnzIlVczj01Qe9hz2EwuEYgu+VjxDsiooYC5etuawSbW6OgSLyCoIdI528bEjlFQSbCYMU4Yw5seo6HOZsUCu3rBSzHbLjOhwh+4/SFwQ7Cs3aCN0K1/+YctOUFpFXEGwd8mx+pfIKgs2EWIpwxpxYdR2O1Q+urk5kW3ZvEbMdsuM6HCH7j9IXBDsKzdrItie2VXl+y/du0dUTv0XkFQR7IqY5rEjlFQSbia4U4Yw5seo6HEOZIq/WqgAAIABJREFUjtQkpQ6HuX0QyxDs6GHSV9j0Fa+6UkReQbDrQpu0TiqvINhMWKUIZ8yJVds4jvzySHXV0TQYR8yhjh3bODp2k3Y3CHZ0/tsGVxaRVxDs6HnVZlAqryDYDPNShDPmxKptHPQsT1915D4dqUmKjcPcNphlCHb0UJmvL979yN1T9ovIKwj2VFxTV0jlFQSbiawU4Yw5sWobx/L7lleC3TShhJhDHTu2cXTsJu1uEOzo/FOO639QaSpeuxSRVxBsO6zJ16XyCoLNhFaKcMacWLWNY8FtC0YnsLk3zxWzKdGxjUPChnifEGxxiusMUK6TaNN0pXYpIq8g2HZYk69L5RUEmwmtFOGMObFqE8e+Z/ZVVxttH0UQc6hjxyaOjl2k3w2CnSQGNPWuvsq27yoVkVcQ7CR51WRUKq8g2AzrUoQz5sSqTRzmdI1tnx0Uc6hjxyaOjl2k3w2CnSQGTZ+RLSKvINhJ8qrJqFReQbAZ1l944QVmy7CqzcShd1G5K43cUZk4cveV9Q+CzVIjuWHvob1V3tt3lorIK0nyIvddSjykcBQr2N/5jlJXXeWXbStXKvUf/oNSH/2oUv/u3yl1ww1KHTjg10ff1ps2KXX66dO9XHmlUoTJt5iJo9+/rnuW59tv7PYmjti2g9mDYAej0rcjbuyGa15x55MSzxm+3IZs7xqPkDYl+pLCUaRg79mj1JlnKrVvn3sobrxxLJQklubfJz6h1P797v30aXnokFLnnFMv2E88McZE2HyKTpyhfU7Txqhx2PWDWodgJwuX+bnN7T/dXvnhklfc+aTUc0ZFToIFl3gkcMvbpBSO4gT7pZeUmj9fqS98wZ3jhx8eiyRdxT755Hg/6mft2nH9X/2Ve199WtL5XP+zUNfPkiVKfeYzdVv4Op04be+j8j3ksUXjyMObjl5AsDsS1383c/4Bc/xGW15x55OSzxn92e7eQ1s8uvccd08pHMUJthZZn6vrSy4ZC+Xzzx8PKhFOBysJ6FlnHa+XWrrjjuNiTTbrCl1l0zbC6Fp04tyw/obqOd6Bw5Hv87s629BO42hokv8mCHayGJkz/NGxoEtbXnHnk7pzBvVZwjlDc5Pity0eKXzqYlMKR1GCTQfL+ecrdfHFXSie3EcTTgJ5xhmT20Kv7d07vt1NdwbIHifYZPeii8YYCatL0TjOvOnMkWDTs7whFo1jiL5XPkOwKypSLFxx+xXVP636c5tNedX1fDL0c0aK2GibTfHQbYbwK4WjKMH+wQ/GYrdiRf+Qbt68WR08OO7vz/6sf39cD3RSoNvcNNDtJz9pF2zCRicEwupSKHHomZ0eHb7i+wHIcTEcuI3UARDYzebuINjN/AhvNb9SR684UmnKqy7nkxLOGcJhaOy+KR6NO2a2UQpHUYKtB4G4illTjH/6058qLY7f/nZTy37bbr55LMBr1oz7abvC3rJl3J5GsLsUShzz+TUtD7FIHQBRuYBgR6XbNlY3D0FTXnU5n5RwzrB5i7neFI+YfvS1JYWjKMG+8MKxmD39dF+6ldIjQ+kcK1UefXTs72c/e9xCm2ATNmrjOviMEsd8fn3o+UPHjQ1oSeoAiEoBBDsq3XXG9J0m/Ry7Ka98zyelnDPqeItV1xSPWD6EsCOFoyjBple5SMz6Fnq96rzzlPr0p5U6fLhvb/X7Hzkyfhb9sY8pRfZ0aRNsuoVObQirS6HEGfrza8IpdQC4cBisDQQ7GJVdO9JzEZzx+TMUPcduyiuf80lJ54yu3IbYrykeIfqP1YcUjqIE+yMfqRdsLYL2b13w6MD75CeVmjt3Ukjr2rbV2fb0Ou1Hr4rR+saNk72YbSa3HF+jNq4D4Zb9z2XV82v6UtdQi9QBEJUPCHZUuuuM0Sdl9VU2verVlFfc+cTut7Rzho0v5npTPGL60deWFI6iBFv/R2yPoNYiaP/aQfnRj8ZCTbOd/cM/OA7Dtjsx1m17ep2a6OW2X6O70aLvFfaiFYuqExTNqTzUInUAROUDgh2V7jpjW3ZvqY4HGoTWlFfc+cTs1zxnmHfKzDY+y9z5gPrgttn1tj3fc4a9f8z1pnjE9KOvLSkcRQn2ggXjpO5y4GzePB6pTa+E0W3wLTS6S7DYBxm3brvwzDNjjPR8zaXM+/y86gR19NhRl12ybCN1AEQFC8GOSnedMboNrq+w6TWvprxqO5/Y54w6eyHruHOEXW/b9D1n2PvHXG+KR0w/+tqSwlGUYC9ePBYzX63dvXt8i5murOnZcsqiDz7OBz1KnLA2lQ0bNqjrrrtOvfUDb1WnzT9NXfp3lzY1z36b1AEQFTgEOyrdnDES6tmfma1+64zfUueff75at26dOnbs2FTzpvNJieeMKQISVBRxnAuOuSlKsLduHQv2cs9HtfSREC2U3K+Zu7qNWRdqua3vW28d+/rgg/UW6f3xt73tneqNb3y3OuWUC9Upv3Gxet2b3qtef+KvK9o21FLEgQzBTp5+dAyc+Ov/TP3T15yi3v4v/qP6jd/8/9TJJ/+eOvnkU6aOj6bzSUnnjORBMRwo4jiHYBsRbVmkAWOurzzprmjSEi2U3K9uS7+6jVkXarmtb8L2p39ab41ORq961WvU7/7uuspH3d/s2RvUq1990tRJqb6n/GqzPZCfekqpN73JjTAIthtPQq308TF79redjw/ufFLKOUOI6s7dZnuceyKSwlHUFTZxum7dWFB9v2rlEw/6VLbra1U+/ba1pdtwJMDcZzbpyrpOrE3RpiuJw1LvqrUB6LFd6gDo4dJ41w9+UKlZjocRBLs33X066HJ8hDqf5HrO6MOnxL7ZHueeYKVwOJ5p3L2VctTdA6VoQBbNUtSnNOH45jeVuuaaPr132/ev/3qMrW5vemZ94om/M3XloMVa/9Ltv9tvv72ui6zrmuKRzHF6yHnddRDsZAFwN9zn+AhxPpE+Z3DHR9M5w529eC05HPE8CGNJCkeRgq1nHNKfyuwSgibCaWYyGnkZsxAWuqrn7hxcc8016pRT/lOrYL/jHX+urqTviA6sNMUjCZTt25Wij6VTwRV2khD4GO1zfIQ4n0ifM+qOj7Zzhg9/sdrW4YhlO6QdKRyzqOPS/v7X//pfav36l9TChYfVU089FRzf008/rf7+7/8+eL9cHA4cOKA++9nnRpgIW127efPmjQaZ6Stp7vc3f/MSNXfu3No+6vqdqXXcwfvd735XPXfokHrmQx9SR/7hH8bNXhbsNq72zJkzEvfdc+aA/8jnnT7HR4jzSY7njLZ8xfb8tLHIK2zuZOtTT8k6pNLnlt8QcEaPB4lw3R+RRUOEzVsduMLOPoVwfGQfopGD0Y9zIVqkcECwmYBJEc6YC1LdZVBNEMMROskqHnVC7iLaGHQWIVN4Ezg+eG5y2ZLVcd6DFCkcEGwmKFKEM+aCVNNrK69//VvUaafVv9Z14onT75oGMRyhk6zj4SLWxBEEO0Km8CZwfPDc5LIl6+PcgyQpHBBsJghShDPmglXTSemNJ71F/drr3jmaGIKeWXMTQwQzGqGjrOMBwY6QAWFM0PFBrzbSGxXmxEJvOOktg52jgJjJ+vjwCB1wNJMFwWb4GXLiXLXmqtF0pP/y//2Xas55c0avcQ3x3WszNFnHA4Jthir75SNHjoymI736c1ePpu593yffpxauWpi9300OZn18NDlubQMOixBrFYJtEaJXh5w4+uMGC7+xEP9564Dm8Itb4jlEYcKH8xefX30MhD4MMtQy5POVyTlwmGxML0OwpzkZ1Qw1cbbu3VqdgFZuWQnBZuKbpBqCnYT2JqNX/o8rq+MFn59tYirOtqGed212pHBAsG2mX16XIpwxF6z6jm13VCegDTs2QLCDMRugIwh2ABLDdrHk75ZUxwt9H3uoZajnK5tv4LAZmVyHYE/yUa0NNXGu/da11QmIvn89VBxVIF5eKAIHBNsOa/L1ezbcUx0v9NnNoZYijg8MnmtNPwg2Q9FQD4AzbzpzdAK6dPX4+9dDxWGHpQgcEGw7rMnXKa9orIce9zHU59hFHB8Q7NbjAYLNUDTEA2D7T7dXJ54V318xQjZEHHUhKQIHBLsutEnrKK/oWNGCvXnXML8ZX8TxAcFuPRYg2AxFQzwA7n7k7urEQ8+vqQwRR11IisABwa4LbdI6yisabKYFm8aADLEUcXzgfNWaehBshqIhHgA3rL+hOvEc+eWREbIh4qgLSRE4INh1oU1aR3lFYz20YNMYkCGWIo4PCHZr6kGwGYqGeADMvXnu6MRz0aqLKlRDxFE5bywUgQOCbUQ0j0WdVzTmg0SbjqEhFo1jiL6bPgOHycb0MgR7mpNRzdASZ8eTO6qrhGWbllWohoajctxaKAIHBNuKavpVnVfL71teHT80FmRoReMYmt+2v8BhMzK5DsGe5KNaG1ri0DNrfVuPnmXrMjQc2m/7twgcEGw7rMnXdV5t2rmpOn7ufPjO5H75OqBx+O6XW3vgaI4IBJvhZ2iJs/TepdUJ58DhAxWqoeGoHLcWisABwbaimn5V59Vzv3iuOn4W37M4vWOeHmgcnrtl1xw4mkMCwWb4GVriXLjywtEJZ/6K+ROIhoZjwnljpQgcEGwjonksmnlFYz/oLtUFyy/IwzkPL0wcHrtl1xQ4mkMCwWb4GVLi0BW1vh1OV9pmGRIO0297uQgcEGw7rMnXzbyisR/6ONp7aG9y33wcMHH47JdbW+BojggEm+FnSIlDkz3oE439/G1IOJhQjKqLwAHBbgpxkm1mXpnvY6/ZuiaJP12Nmji69pHDfsDRHAUINsPPkBJn1f2rKsHec3DPBKIh4Zhw3FopAgcE24pq+lUzr8zn2F/a+KX0znl4YOLw2C27psDRHBIINsPPkBKHPlpAV9gLblswhWZIOKacNyqKwAHBNiKax6KdV/o5tp6LPw8v272wcbTvkWcL4GiOCwSb4WcoiWNeFdBMZ3YZCg7bb3u9CBwQbDusydftvDLnFd//s/3J/XN1wMbhul9u7YCjOSIQbIafoSSO+dxNzx9uQhoKDtPnuuUicECw60KbtM7OK/N97CHNK27jSEpqD+PA0UweBJvhZyiJY14RPPDjB6bQDAXHlONWRRE4INhWVNOv2nllfvGOZj8bSrFxDMVv20/gsBmZXIdgT/JRrQ0lcS5bc9no+fW5XzlX1X3Ldyg4KuKZhSJwQLCZ6Karrsur87563uiYGtJz7Doc6Vjtbhk4mrmDYDP8DCVx9OtcV6+9uhbJUHDUOm9UFoEDgm1ENI/FuryiL3bp46run+A8PJ/0og7HZIthrAFHc5wg2Aw/Q0gcugWuTyyrH1xdi2QIOGodtyqLwAHBtqKafrUur+jZtT6u1j+6Pr2TDh7U4XDYLbsmwNEcEgg2w88QEocmSdEnlroBZwRtCDiYEExUF4EDgj0R0xxW6vLK5R/hHHw3fajDYW4fyjJwNEcKgs3wM4TEuf7b11eCzd26GwIOJgQT1UXggGBPxDSHFS6v9D/Ci+5alIObrT5wOFp3zKwBcDQHBILN8DOExJl789yRYDcNjhkCDiYEE9VF4IBgT8Q0hxUurxZ+Y+Ho2KLBnEMoHI4h+G76CBwmG9PLEOxpTkY1uSeO6+snueNg6J+qLgIHBHsqrqkruLwyX5fcundrajdb7XM4WnfMrAFwNAcEgs3wk3vi0DNrfdvO/uCHCSl3HKavTctF4IBgN4U4yTYur1yPryRO1xjlcNQ0zboKOJrDA8Fm+Mk9cejjBFqwDz1/iEGBQWcsMSk2QLBTsN5okzvOj/zySHV8LdmwpLGPHDZyOHLwzccH4GhmC4LN8JN74tCHPkiw56+YzyAYV+eOo9F5Y2MROCDYRkTzWGzKK/0hkLZjLAckTThy8M/VB+BoZgqCzfCTc+I8+/Nnq//+l967lEEwrs4ZR6Pj1sYicECwraimX23Kq2WbllXH2b5n9qV3tsGDJhwNu2W3CTiaQwLBZvjJOXHMD37c/cjdDIJxdc44Gh23NhaBA4JtRTX9alNeDelDIE040rPs7gFwNHMFwWb4yTlxzBGsNFq8qeSMo8lve1sROCDYdliTrzfl1Z6De6or7Nw/BNKEIznJHg4ARzNZEGyGn5wTR3/wgz5S0FZyxtHmu7m9CBwQbDOkWSy35ZXLXAc5AGnDkYOPLj4ARzNLEGyGn5wTR48Od5mFKWccDPW11UXggGDXxjZlZVteucwmmNJ/bbsNh26X+y9wNEcIgs3wk2vi+M5znCsOhna2uggcEGw2vqk2tOWVOV9/zh8CacORil9fu8DRzBgEm+En18TxPYHkioOhna0uAgcEm41vqg1teeX7D3KuOFL55Wu3LR6+/aVqL4UDgs1EVIpwxpxz9Q3rb6gGwhw9drR1v1xxtDpuNSgCBwTbimr61ba8oo/q6EdQ9J3sXEsbjlz9tv0CDpuRyXUI9iQf1VquiaMHwVzy9UsqX5sWcsXR5HPdtiJwQLDrQpu0ziWv6OM6JNp07OVaXHDk6rvpF3CYbEwvQ7CnORnV5Jg4ew/trf7bp6lJXUqOOFz8ttsUgQOCbYc1+bpLXt3yvVuq427HkzuS+1zngAuOuv1yqwOO5ohAsBl+ckyczbs2VyeOpg9+mJByxGH657qcJY7rr1dq1qzx32mntUOBYLdzFLmFS16ZExW5HneRYSgXHLF96mIPOJpZg2Az/OSYOOZ/+nS17VJyxOHit90mSxxvf7tS999vu8qvQ7B5bhJtcckr+riOfo7dNhVwIhgQ7FTEM3Zd8orZtbEags3QI0U4Y86pusuztBxxOIG1GmWH4667lPrABywvW1Yh2C0Exd/smlcXLL9gJNr0QZAciyuOHH03fQIOk43pZQj2NCejmtwSxxytSiPFXUtuOFz9tttlh4PE+hWvGIu261U2BNsOa/J117wy386gT2/mVlxx5Oa37Q9w2IxMrs8igvCXPwdLv75Uzb589ujvL1b8BWImnLeTh8nxNX2sPP3000odO6Ze+pu/US+95jXqpe98R23durUxLnvmzBk97949Z05jO20Dv/kcl3+58i+r4++6FdchfsLHH3K/PvdxhX38XDyxRAmTU6FZlvRztA07Nji7lhsOZ8ethtFx6MFk9q/l12j14Yfdbo/jCruOvaR1rnllTqBCH9/JrbjiyM1v2x/gsBmZXIdgT/JRreWWOF1vyeWGoyLYcyF7HGee2Y4Igt3OUeQWPnl1xufPGP3TfMXtV0T2st2cD4723tK1AI5m7iHYDD+5JY4e9EJf6vIpueHw8d1smz2O973PdLd+GYJdz0vCWp+8IqGmu1xnf/HshB7Xm/bBUd9DHrXA0RwHCDbDT06JY36X13XCFA0rJxzapy6/2eHQA82OHFFq3jylvvGNdlgQ7HaOIrfwyatV96+qHku1fYc+MozRM/XYNiXs+cRDwn6oPqVwQLCZCEkRzphrrDYnTFmzdU1jW3tjTjhs33zWs8Px/vcr9eY3K3XqqUp97WtuUCDYbjxFbOWTVzlPoOKDIyK93qaAo5kyCDbDT06JY06Ysu+ZfYzH9dU54aj30K22CBwQbLdgR2zlk1c5T6DigyMivd6mgKOZMgg2w09OiaMnTJl36zzGW746Jxy8l+1bisABwW4PdOQWvnk1f8X80W3x3CZQ8cURmWZnc8DRTBUEm+Enl8QxJ0y5/tvXM97y1bng4D1021IEDgi2W7AjtvLNK/NtDZfP28aC4osjll++doCjmTEINsNPLoljvv/p+/yaoOWCg6HZuboIHBBs53jHauibV/Txjy7zIUjj8cUh7U/X/oGjmTkINsNPLolzx7Y7ep0gcsHB0OxcXQQOCLZzvGM19M0r8x/o1Q+ujuVmqx1fHK0dJmoAHM3EQ7AZfnJJHLoNrv+jp9vjviUXHL5+2+2LwAHBtsOafL1LXunjcdFdi5L7rx3ogkPvm9MvcDRHA4LN8JNL4tBAMzpB0MCzLiUXHF18N/cpAgcE2wxpFstd8mrhNxaOjsm5N8/NAgM50QVHNs4bjgCHQUbNIgS7hhSqyiFx9v9sf3V1Ta92dSk54Ojit71PETgg2HZYk693ySuaS1xfZdOkRjmULjhy8Nv2AThsRibXIdiTfFRrOSTOpp2bqhMDDXbpUnLA0cVve58icECw7bAmX++SV+ZxSWNMcihdcOTgt+0DcNiMTK5DsCf5qNZySJwQ/8nngKMitcdCETgg2D0yQGbXLnkV4s5XaDRdcIT2IUR/wNHMIgSb4SeHxKEPfdCtt/O+eh7jZXt1DjjavWxvUQQOCHZ7oCO36JpXfceWhIbZFUdoP/r2BxzNDEKwGX5ySBz9nOzqtVczXrZX54Cj3cv2FkXggGC3Bzpyi655de23rq0eV3V5eyM0zK44QvvRtz/gaGYQgs3wkzpxtu7dWp0Q+rzvmRoHQ693dRE4INjecZfeoWtemfMjrH90vbSbrf13xdHaceQGwNFMOASb4Sd14tBJQF9h9zkhpMbB0OtdXQQOCLZ33KV36JpX5hf07n7kbmk3W/vviqO148gNgKOZcAg2w0/qxFl679JKsI/88gjjZXt1ahztHrq1KAIHBNst2BFbdc0rmkdc/0O9+J7FET2uN9UVR31v6WqBo5l7CDbDT+rEWXDbgtEJgb4O1KekxtHHd3PfInBAsM2QZrHcJ6/oi10k2n2P0RBE9MERwn6oPoCjmUkINsNPysShK2r93/uSDUsYD92qU+Jw89CtVRE4INhuwY7Yqk9eLdu0rDpOn/35sxG9njbVB8d0b+lqgKOZewg2w0/KxDEnZuj7fCwlDobaTtVF4IBgd4q95E598mrj4xsrwe57nPbF2AdHX9sh9weOZjYh2Aw/KRPHHIFKg1v6lJQ4+vht71sEDgi2Hdbk633yatsT2yrBXnX/qqRY+uBI6rhlHDgsQqxVCLZFiF5NmTj6Hc+zv3i26vuOZ0ocmssQv0XggGCHSIWgffTNq3O+fM5ItK+4/Yqgfvl21heHrz2p9sDRzCwEm+EnZeLoWZToq0B9S0ocfX039y8CBwTbDGkWy33zioSaxpv0mY0wBBF9cYTwIUQfwNHMIgSb4SdV4oSepzgVDobWztVF4IBgd46/1I598yrEfP8hsPXFEcKHEH0ARzOLEGyGn1SJYw446/qFLhNSKhymDyGWi8ABwQ6RCkH76JtX5vGa8stdfXEEJbVHZ8DRTB4Em+EnVeKY/7HvemoX4517dSoc7h66tSwCBwTbLdgRW/XNK/OO2PL7lkf0fNJUXxyTvaVbA45m7iHYDD+pEif0M7FUOBhaO1cXgQOC3Tn+UjuGyKu5N88dPccOMeakK84QOLraDrkfcDSzCcFm+EmVOOd+5dygo05T4WBo7VxdBA4Iduf4S+0YIq9CvtXRFWcIHF1th9wPOJrZhGAz/KRInO0/3T4Saxp1Guq9zhQ4GEp7VReBA4LdKwckdg6RV2u2rqmO2y27t0i42dpnCBytRiI0AI5mkiHYDD8pEsccwNLnC10mpBQ4TPuhlovAAcEOlQ7B+gmRVxLHrS/AEDh8bUq0B45mViHYDD8pEscccHbo+UOMZ37VKXD4eejWuggcEGy3YEdsFSKvzLn/b1h/Q0Tvj5sKgeN4b+mWgKOZewg2w0+KxNFf/6GJU0KVFDhC+W72UwQOCLYZ0iyWQ+UVfbGLHmXRV/ZSlFA4Uvhu2gQOk43pZQj2NCejmhSJo7/QRYNYQpUUOEL5bvZTBA4IthnSLJZD5RVdWevj97lfPBcdWygc0R23DAKHRYi1CsG2CNGrsRNn696t1QG/+sHV2o3ev7Fx9HaY6aAIHBBsJrrpqkPlFU1ypAU7xIRHvoyEwuFrN3R74GhmFILN8BM7cejzfPqADzXgjKDFxsHQ2bu6CBwQ7N55ELqDUHn1wI8fqI7fFDOehcIRml/f/oCjmTEINsNP7MRZeu/S6oA/euwo45V/dWwc/h667VEEDgi2W7AjtgqVV/RVPf0P9+J7FkdEMDYVCkd0xy2DwGERYq1CsC1C9GrsxKHBKnTA0+CVkCU2jpC+m30VgQOCbYY0i+WQeaUHjYY+hl2IConDxZ5UG+BoZhaCzfATM3Hoilr/d75kwxLGo27VMXF089BtryJwQLDdgh2xVci8WrZpWXUcxx54FhJHRPqnTAHHFCUTFRDsCTqOr8RMnM27NlcHOj3LDlli4gjpt91XETgg2HZYk6+HzKsNOzaIHcdtRIXE0WZLcjtwNLMLwWb4iZk45ghTmjUpZImJI6Tfdl9F4IBg22FNvh4yr7Y9sa0S7JBveriQFBKHiz2pNsDRzCwEm+EnZuKY73DS4JWQJSaOkH7bfRWBA4JthzX5eui80o+2Qs6l4EJSaBwuNiXaAEczqxBshp+YiaNnSbrk65cw3nSvjomju5ftexaBA4LdHujILULnFX1ik0Q75GyFLpSExuFiU6INcDSzCsFm+ImVOM/+/NnqNhq92hW6xMIR2m+7v2xx3HefUv/6Xyt1wgm2y9PrEOxpThLXhM6rW753S3U87//Z/mjoQuOI5rhlCDgsQqxVCLZFiF6NlTjml35CDzgjLLFwaN6kfrPEsW6dUu94h1Jf+5pSRx3enYdgS6VH535D55U5gDTmjGehcXQmtOeOwNFMIASb4SdW4tDgFP3ciwathC6xcIT22+4vOxwHDyp12mlKPfWU7Sq/DsHmuUm0JXRe7XpqV3U8r9yyMhqq0DiiOW4ZAg6LEGsVgm0RoldjJQ4NTiHBPvuLZ6vQA84ISywcmjep3+xwXHGFUueeq9RJJ41vh991Vzt0CHY7R5FbSOTVuV85d3RMX3H7FdHQSOCI5rxhCDgMMmoWZxFB+EvHwel/cbqaffls9e9v+PeIQ0a5WHOsjKroWDl8+LBSp56qXli3Tr3wwgtKkVifcIJ66aWXGmO4Z84cpWbNUruX/qDDAAAgAElEQVTnzGlsh+Mx3fEYgvvzF58/OqY/dM2HEOeMjukQsU3dB66wmTMzBUa6HHr+UHX7jGZJkigxcEj4bfcZHcesWSNxJYGd+NOO2YPMqF1bwRV2G0PRt0vk1fL7llfH9d5De6NgksARxXHLCHBYhFirDmcZa4+WVRDeQpCxeePjG6sDW2LAGZlCPAzCQy7aAm2v19mCYNexkrRO4vgwB57F+nKXBI4UgQGOZtYh2Aw/MRLHHHC2/afbGU/6VcfA0c9Dt72zw2ELtL1eBwuCXcdK0jqJvNpzcE/1j3isgWcSOFIEBjiaWYdgM/zESBzpAWcELQYOhsKg1dnhoFvieqDZy8+wWwFDsFspit1AKq9iDzyTwlFKPErBAcFmIhnjAJh789zRf+KXrbmM8aJ/dQwc/b1s7yE7HFqk6cqaxHvt2nYQEOx2jiK3kMqrq9dePTq2SbhjFCkcMXw3bQCHycb0MgR7mpNRjXTiHDh8oLptRoNUpIo0Dim/7X6LwAHBtsOafF0qr+hWuJ5fgW6RSxcpHNJ+2/0Dh83I5DoEe5KPak06ccwZziRnRJLGUREmvFAEDgi2cJb4dy+VV+bxHWPgmRQOf0b77QEczfxBsBl+pBPH/A+cZkeSKtI4pPy2+y0CBwTbDmvydam8onnE9RW25B00TaAUDt1/rF/gaGYags3wI504i+5aNDqgz/nyOYwHYaqlcYTxsr2XInBAsNsDHbmFZF6d99XzRse45BgVTZckDm0jxi9wNLMMwWb4kU6cWAezNA6GvuDVReCAYAfPi74dSuZVrH/KiQNJHH059tkfOJrZgmAz/EgmTszbZZI4GOpEqovAAcEWyY0+nUrmVazHXoRfEkcffn33BY5mxiDYDD+SiWMOSJEccEbQJHEw1IlUF4EDgi2SG306lcwr8ziXHngmiaMPv777AkczYxBshh/JxMF/3gzpDdWS8WgwG3YTBDssnwF6k8wr3EnzD5BkPPy96b6HFA4INhMTKcLJHJ5tMaQ3VEvGo8Fs2E0Q7LB8BuhNOq/0WJWF31gYwFu+C2kcvOWwW4CjmU8INsOPZOLogxijRxnya6ol41FjTqYKgi3Da49epfNK/3MuPeOZNI4eFHvtChzNdEGwGX6kEifWDGcalhQO3X+s3yJwQLBjpYuzHem8Mh9/SX5qUxqHM6E9GwJHM4EQbIYfqcQxB6JIfVLThCSFw7QRY7kIHBDsGKniZUM6r8zjff2j671882ksjcPHlz5tgaOZPQg2w49U4pj/cdOgFOkihUPab7v/InBAsO2wJl+Xzqtnf/5sNePZiu+vEMMrjUPMcatj4LAIsVYh2BYhelUqcfRXfC5YfoE2JforhUPU6ZrOi8ABwa6JbNqqGHm14LYF4jOexcARI1LA0cwyBJvhRypxLlx5ofjBa0KSwmHaiLFcBA4IdoxU8bIRI6+u//b1o2OeBptKlRg4pHw3+wUOk43pZQj2NCejGonEMW+PLdu0jLEctloCR1gP3XorAgcE2y3YEVvFyCv6+If+EMi+Z/aJoIuBQ8Rxq1PgsAixViHYFiF6VSJxNj6+sTpwYww4IywSODRHMX+LwAHBjpkyTrZi5NXmXZur415qZsMYOJwI7dkIOJoJhGAz/EgkDk1PqP/T3v7T7YzlsNUSOMJ66NZbETgg2G7BjtgqRl7tObinOu5p0KlEiYFDwm+7T+CwGZlch2BP8lGtSSSOfpZ19hfPVi+8+EJlS3JBAoekv1zfReCAYHPhTVYfK69o4hT6Z50mUpEosXBI+G72CRwmG9PLEOxpTkY1EomjB5xJT1NoQpLAYfYfa7kIHBDsWOnibCdWXl1x+xUjwZ536zxn33waxsLh41OXtsDRzBoEm+EndOI894vnqttisQacEbTQOBi6xKuLwAHBFs8TXwOx8soceCYx/0IsHL78+rYHjmbGINgMP6ETx5zxKNaAM4IWGgdDl3h1ETgg2OJ54msgVl5JDzyLhcOXX9/2wNHMGASb4Sd04pgDzrY9sY2xGr46NI7wHrr1WAQOCLZbsCO2ipVXu57aVd1hW3X/quAIY+EI7rjVIXBYhFirEGyLEL0aOnFSDDgjLKFxaH5i/xaBA4IdO21a7cXMK/2VPomBZzFxtJLaowFwNJMHwWb4CZ04enrCS75+CWNRpjo0Dhkv23stAgcEuz3QkVvEzCv6nC6NFJeYljgmDskQAUczuxBshp+QiXP02NHqdtjSe5cyFmWqQ+KQ8dCt1yJwQLDdgh2xVcy8oo9/6HkYaBBqyBITR0i/7b6Aw2Zkch2CPclHtRYyccwBJxt2bKhsxFgIiSOGv5yNInBAsLnwJquPmVeSMx3GxCEZLOBoZheCzfATMnFoOkL9nzWJd8wSEkdMv21bReCAYNthTb4eM69osKk+D6x+cHVQ7DFxBHXc6gw4LEKsVQi2RYheDZk4i+9ZXB2osWY4k8Ch+0zxGzIeKfwf2YRgJ6OeMxw7r7Rg0yDUkCU2jpC+m30Bh8nG9DIEe5qTUU3IxLlo1UUjwaaBZ7FLSByxfTftFYEDgm2GNIvl2HlFg05JtOevmB8Uf2wcQZ03OgMOg4yaRQh2DSlUFSpx6Ipa/1e9ZMMSxppcdSgcch669VwEDgi2W7AjtoqdVzToVJ8PaDBqqBIbRyi/7X6Aw2Zkch2CPclHtRYqcR748QPVAUqTp8QuoXDE9tu2VwQOCLYd1uTrsfOKZjnUgh1yxsPYOKQCBxzNzEKwGX5CJY55gMYeIU7QQuFgaIpWXQQOCHa0fHE1FDuvpP6Bj43DlV/fdsDRzBgEm+EnVOLQhz70f9Qhb4Exbk9Vh8Ix1XHkiiJwQLAjZ027udh5Zc7JEPIRWWwc7cx2awEczbxBsBl+QiWO1CATxu2p6lA4pjqOXFEEDgh25KxpN5cir/SshyEHoabA0c6ufwvgaOYMgs3wEypxzlp61ugK+4b1NzCWZKtD4ZD1sr33InBAsNsDHblFirzSr3nSuSHUa54pcEiECjiaWYVgM/yESBxzogSJL/Qwrk9Uh8Ax0WGilSJwQLATZQ9vNkVemV/uCzWRUgocPKvdtwBHM3cQbIafEIljfgN7/aPrGUuy1SFwyHro1nsROCDYbsGO2CpFXpnnhVAjxVPgkAgTcDSzCsFm+AmROMvvW14NODv0/CHGkmx1CByyHrr1XgQOCLZbsCO2SpFX9OEPPRCVBqWGKClwhPDb7gM4bEYm1yHYk3xUayES54rbrxgdmPQd3FQlBI5Uvpt2i8ABwTZDmsVyqryad+u80blh4TcWBuEhFY4gzhudAIdBRs0iBLuGFKoKkTjnfuXc0UFJwp2qhMCRynfTblY47r9fqVmz6v/27DHdnlyGYE/ykcFaqry69lvXjs4N53z5nCAspMIRxHmjE+AwyKhZhGDXkEJVfRNn/8/2jw5IuvVFt8ZTlb44Uvlt280Kx+WXK/XYY5Mu/uhHSr33vZN19hoE22Yk+XqqvFq5ZWV1ftj11K7ePKTC0dtxqwPgsAixViHYFiF6tW/imN/Aps9rpip9caTy27abFY6DB233lLrqKqUWLZquN2sg2CYbWSynyqvQA89S4QgdROBoZhSCzfDTN3HMb2DvOdhwm5SxH6q6L45QfvTtJ3scp56q1M6dzTAh2M38JNiaKq8OHD5QXWGv2bqmN/JUOHo7bnUAHBYh1uosIgh/4Tm4+MsXq9mXz1Yf/NwHwe8Ac8w6TqpV+1j5/ve/r375yCPqpd/+bfX88883xnrPnDmj596758xpbGfbwHr44zMHTj+86MOjc8SnlnwK+TDAc0SKHMIVdnUqnlygYPQp+hvYl66+tE83vffti6O3A4E6iI6DG1RWh4duh3/uc3VbJutwhT3JRwZr0fPKwHzZmstGV9k0YrxvSYmjr+/m/sBhsjG9DMGe5mRU0ydxzG9g3/K9WxgLcar74IjjoZuVrHHQ7XAadNZWINhtDEXfnjKvVnx/RXVbnG6R9ykpcfTx294XOGxGJtch2JN8VGt9EscccBZqJqPKMc+FPjg8TYk2zxYHCTUJtkuBYLuwFLVNyrza+PjGSrD7nidS4ggZMOBoZhOCzfDTJ3Ek5gpm3Gyt7oOjtfOIDbLFQbfDr3B8zx6CHTFj3EylzCvzWwOrH1zt5jDTKiUOxqVO1cDRTBsEm+GnT+Lor/GcedOZwb7Gw7jZWt0HR2vnERtki8P1djhxBcGOmDFuplLnlf6a3/Xfvt7NYaZVahyMW97VwNFMGQSb4adP4ugBZyG/d8u42VrdB0dr5xEbFIEDgh0xY9xMpc4rfa6Yv2K+m8NMq9Q4GLe8q4GjmTIINsNP18QxB5zRlXbq0hVHar9t+0XggGDbYU2+njqvlt67tHqOffTY0c58pMbR2XFrR+CwCLFWIdgWIXq1a+Js3bu1OgDpWXbq0hVHar9t+0XggGDbYU2+njqvzAmW+nyCNzWOUIEEjmYmIdgMP10TZ8OODZVg9zkAGbe8q7vi8DYkvEMROCDYwlni333qvAr1RklqHP7M1+8BHPW86FoItmbC+u2aOPTetf7WLX33NnXpiiO137b9InBAsO2wJl9PnVdHfnmkOl/Q7fGuJTWOrn7b+wGHzcjkOgR7ko9qrWvi6G9gh5i9qHKmx0JXHD1MiuxaBA4Itkhu9Ok0h7yiAWf0T36fb2PngKNPHPS+wKGZqP+FYNfzMprbl9nUWJ3DN7BNB3EAmGwkXoZgJw7AtPkcjg/9beyzv3h259dAc8Axza5/DXA0cwbBZvjpkjjmN7Dpe7c5lC44cvDb9qEIHBBsO6zJ13PIK5o0RT9G6/pt7BxwhAgmcDSzCMFm+OmSOOY3blN+A9uE1AWHuX8uy0XggGDnkk6VHznklXne6DpFaQ44KlJ7LABHM3kQbIafLokT4j9lxp3O1V1wdDYmuGMROCDYghnSresc8irEnbkccHSLwORewDHJh70GwbYZeXm9S+LQ9IJ0a6vPsyjGnc7VXXB0Nia4YxE4INiCGdKt61zySo99WXTXok5AcsHRyXljJ+AwyKhZhGDXkEJVXRJHj/a85OuXML3Gr+6CI76X7RaLwAHBbg905Ba55BWNEKd/9i9YfkEnBnLB0cl5YyfgMMioWYRg15BCVb6JQ9MK6oEjfd6nZNzpXO2Lo7Mh4R2LwAHBFs4S/+5zyStz/gZ6N9u35ILD12+7PXDYjEyuQ7An+ajWfBPngR8/UAl214EjlfGAC744ApoO2lUROCDYQXMiRGe55JU5Q2KX80cuOPrGBDiaGYRgM/z4Jg4dZPoKmw6+XIovjlz8tv0oAgcE2w5r8vVc8sr8h7/LNwhywdE3oMDRzCAEm+HHN3GWbVpWCXafr+4w7nSu9sXR2ZDwjkXggGALZ4l/97nklfmVvyUblngDyQWHt+PWDsBhEWKtQrAtQvSqb+L0HTSi7Yb+9cUR2n6o/orAAcEOlQ7B+skprxbctmD0T3+XQas54egTHOBoZg+CzfDjmzjnfPmc0cHW9bUMxo3e1b44ehsU6qAIHBBsoezo3m1OeaVfCz1r6VneU5TmhKN7NPwH+/axJbmvVDwg2EzUfAjfc3BPdTt81f2rmB7TVPvgSOOhm9UicECw3YIdsVVOeWVOvLTtiW1eLOSEw8txqzFwWIRYqxBsixC96pM45jdtc5mStAsOvU+Ovz7xyNH/kU8Q7OxCk1NebXx8Y/WPv+9I8Zxw9AkycDSzB8Fm+PFJHPrQhx4hTlfbORUfHDn5bftSBA4Ith3W5Os55dWBwweq88jy+5Z7cZMTDi/HrcbAYRFirUKwLUL0qk/i6M/j0XPs3IoPjtx8N/0pAgcE2wxpFsu55ZWeovSK26/w4ic3HF7OG42BwyCjZhGCXUMKVfkkjp6StM8H6Bk3elf74OhtTLCDInBAsAUzpFvXueUVCTXdrZt36zwvQLnh8HLeaAwcBhk1ixDsGlKoyjVxaBpBfTs8pylJNSxXHLp9rr9F4IBgZ5deueWVOUXpc794zpmv3HA4O241BA6LEGsVgm0RolddE2fL7i2VYPsOFNG2JH9dcUj6EKLvInBAsEOkQtA+csurrlOU5oaja5CAo5k5CDbDj2vimFOSrn90PdNbumpXHOk8dLNcBA4ItluwI7bKLa/MCwCfKUpzw9E1hMDRzBwEm+HHNXFoGkF9S7zLV3YY88GqXXEEMyjUURE4INhC2dG929zyyvzq3w3rb3AGlhsOZ8ethsBhEWKtQrAtQvSqa+JctuaykWDTwLMciyuOHH03fSoCBwTbDGkWyznm1UWrLhqdU+jXteSIw9V3sx1wmGxML0OwpzkZ1bgmztlfPHt0cPm+hsGYDV7tiiO44cAdFoEDgh04K/p3l2NeLb5n8eic4jNFaY44ukQHOJpZg2Az/LgkjjnRwYrvr2B6SlvtgiOth27Wi8ABwXYLdsRWOeaVORHTjid3OLGRIw4nx61GwGERYq1CsC1C9KpL4mzauWn0nzA9w85tSlIfHLptzr8u8cjZ/5FvEOzsQpRjXnWZojRHHF2CDRzNrEGwGX5cEsecrD+3KUk1LBccum3Ov0XggGBnl2I55pV5546utl1Kjjhc/LbbAIfNyOQ6BHuSj2rNJXH05/BynJJUA3HBodvm/FsEDgh2dimWa17pKUpdP9ebKw7fgANHM2MQbIYfl8TRU5J2+eA8YzZ4tQuO4EYFOiwCBwRbIDP6dZlrXtE0x/So7YLlFzgBzBWHk/NGI+AwyKhZhGDXkEJVbYljvi+Z45SkGlYbDt0u998icECws0uzXPNq2aZl1fgYl/kdcsXhG3DgaGYMgs3w05Y4D/z4geqAynFKUg2rDYdul/tvETgg2NmlWa555TtFaa44fAMOHM2MQbAZftoSxzygcpySVMNqw6Hb5f5bBA4IdnZplmtebd612euCIFccvgEHjmbGINgMP22J43vLijEjXt2GQ9yBQAaKwAHBDpQN4brJNa98H7nlisM3UsDRzBgEm+GnLXG6freWMSdW3YZDzHDgjovAAcEOnBX9u8s5r/SgVhqA1lZyxtHmu7kdOEw2ppch2NOcjGraEke/dpHrlKQaVhsO3S733yJwQLCzS7Oc8+rab107ui3u8tpozjh8gg4czWxBsBl+mhLHnNhg+X3LmR7yqG7CkYeHbl5kh2PtWqVOOEGpWbPGv3fd1Q4Egt3OUeQW2eWVgd+corRtYqaccRiQWheBo5kiCDbDT1PimFMH5jzgjKA14WCgZ1mdHQ4Say3S9EvrbQWC3cZQ9O3Z5ZXBgDnwrO3b2DnjMCC1LgJHM0UQbIafpsShg0d/A3vr3q1MD3lUN+HIw0M3L7LD8da3KnX48Nj5F19U6qST2oFAsNs5itwiu7wy8NOHP/R5hqZBbio542jy294GHDYjk+sQ7Ek+qrWmxOny+buq48gLTTgiu9LLXHY4vvY1pT7+caWOHlXq+uuVovW2AsFuYyj69uzyymKAPrFJok3TIDeV3HE0+W5uAw6TjenlWUQQ/vw4+KO//CM1+/LZ6qzrzwJ3hebP9KEyrtHHyv79+9VL/+2/qRff/Gb10urVat++fa25sGfOnNEz791z5rS21Xbw63dslsYXzjUzO/52PuMKmzkzE1Fc0f/10pV27qUJR+6+m/5Fx0GDyer+tFNHjih1441KrVih1OzZSu3Zo7fwv7jC5rlJtCV6XnnipGmP6QqbzjkvvPgCu3fuOFjHrQ3AYRFirUKwLUL0Kpc4Ps+VdF8pfzkcKX3qYjs7HH/yJ8dFevlypX7/99thQbDbOYrcIru8svDf+fCd1XNsmg6ZK7nj4Py264HDZmRyHYI9yUe1xiWOOXIz5znENRAOh94+lN/scJijwuk59ite0U4lBLudo8gtsssrC/+mnZsqwW463+SOw4LFrgIHS81oAwSb4YdLHPPdyH3P7GP2zqeaw5GPh26eZIcDr3W5BS7zVtnllcXXoecPVYLdNOdD7jgsWOwqcLDUjDZAsBl+uMTxmX2I6TpqNYcjqhMBjGWHQ797rSdOoYlU2gqusNsYir49u7yqYeC8r543Eu1Fdy2q2TquGgIO1nljA3AYZNQsQrBrSKEqLnF85vdluo5azeGI6kQAY0XggGAHyISwXQwhr1y+WzAEHC6RA45mliDYDD91ieP7BR2m66jVdTiiOhDIWBE4INiBsiFcN0PIK5cvAw4Bh0vUgKOZJQg2w09d4gxtwBlBq8PBQM66uggcEOzscmwIebVhx4bqOTY38GwIOFyCDxzNLEGwGX7qEocOFj1VIM0nPoRSh2MIfts+FoEDgm2HNfn6EPKKpj/W5x1uTvEh4HAJNnA0swTBZvipSxzz1hTdHh9CqcMxBL9tH4vAAcG2w5p8fQh5RROmaMFesmFJLWdDwFHruFUJHBYh1ioE2yJEr9Yljh4hPvfmubpZ9r91OLJ3usbBInBAsGsim7ZqKHl10aqLRqJ96epLawkbCo5a541K4DDIqFmEYNeQQlV1iaNHiF+25jJmr/yq63Dk52W7R0XggGC3Bzpyi6HkFb3SRVfZFyy/oJahoeCodd6oBA6DjJpFCHYNKVRlJ86RXx6pbkut+P4KZq/8qm0c+Xno5lEROCDYbsGO2GooebXq/lXV+YcmU7HLUHDYftvrwGEzMrkOwZ7ko1qzE8ecInAoA84IjI2jAjiwhSJwQLCzy7qh5NWW3Vsqwa4bKT4UHG0JABzNDEGwGX7sxHGdhJ/pLlm1jSOZIz0NF4EDgt0zC8LvPpS8Mj86VDdSfCg42iIIHM0MQbAZfuzE0Z+5O/OmMxs/c8d0l6zaxpHMkZ6Gi8ABwe6ZBeF3H1JeNX3Wd0g4mqIIHE3sKAXBZvixE+eSr18yuiVFA8+GVGwcQ/Ld9LUIHBBsM6RZLA8prxbctmB0DqJfuwwJh+27uQ4cJhvTyxDsaU5GNXbinPPlc0YHy/Xfvp7ZI89qG0eeXrZ7VQQOCHZ7oCO3GFJeLb5n8egcdPYXz566yzckHE0hBo4mdnCFzbJjJg59RlNPXECjNYdUTBxD8tv2tQgcEGw7rMnXh5RXqx9cXZ2H6Jm2WYaEw/TbXgYOm5HJdVxhT/JRrZmJY44QX//o+qrNEBZMHEPwl/OxCBwQbC68yeqHlFfmecgeKT4kHE3BBo4mdnCFzbJjJk7Tf7ZsB5lsMHFk4lInN4rAAcHuFHvJnYaUV3sP7a2usO07fUPC0RRP4GhiB4LNsmMmjn52RKM0aV7fIRUTx5D8tn0tAgcE2w5r8vWh5RU3lmZoOLjAAwfHzLget8QZfszE0fP41o3OZHbPptrEkY1THRwpAgcEu0PkZXcZWl5xb6sMDQcXVeDgmBnXQ7AZfszEaXr/kdk9m2oTRzZOdXCkCBwQ7A6Rl91laHnFzQcxNBxcVIGDY2ZcD8Fm+NGJY84wRM+yh1Y0jqH5bftbBA4Ith3W5OtDyytuxsU2HN/5jlJXXTVJ98GDSl1zjVJnnjn+++xnldq5c7KNxNqRI0p95StKfeITSn30o0p95jNKffe7Y0smjiuvVIr8HmIxcYT0H4LNsKkJ37xrczXQY2gjxAmaxsHAHEx1ETgg2Nnl29Dyihsp3oRjz56xIO/bd5z+Z55R6txzlTr99Mm/M85Q6rHHjrcLvXTsmFJ/9meTNrUPt92m1BNPPFGZpEX6Z4L8H1ppikcfLBBshj1NuDlCnN7HHlrROIbmt+1vETgg2HZYk68PLa/oS116ToiVW1ZW/HE4XnpJqfnzlfrCF6qmowW6wiWh/K//Vamf/UwpEtIbbxzXXVr/ye3JDjqu/d3fjW1cdJFS+h+Ip59W6vLLx/W7d092vGTJ+Ap8sjb/NS4efT2HYDMMasJpZjM6QGh05hCLxjFE302fi8ABwTZDmsXyEPPq3K+cOzon0TeydeFwrF07FkItjrr9H//xuJ5ui+ty9Oi4jm5TSxV9df3II5MWdu0a2166dLKerrLpHwvCMaTCxaMvBgg2w6AmXM/fS6Mzh1g0jiH6bvpcBA4IthnSLJaHmFcLv7FwJNgXLL+g4rAOB11dn3++UhdfXDVrXKBnyySOdKtcqtAtd7JBvpmF1qn+wgvN2vEyXY0TDnuf6Zb51NTFI4R3wQV78+bNIfxK3gcRTu9c69tPNDpziEUqcWJzUQQOCHbstGm1N8S8WrZpWXVeOnrs6AhjHY4f/GAsgitWtNKgnn9eqb/6q3F7um0tVbRg2/1rwT7rLHuLUuQ/iTnhGUqpi0cI31sFu250YZPhp556MbuRh6a/riMPifCte7dWB0bdN2jNfnNdlkqc2HiLwAHBjp02rfaGmFc0Lam+kKBBsVTqcOhn0m1Ct3GjUh/5yFgU6dm2ZPnUp8Z29u6dtLJt27ieBN0uW7aMt91wg70l3/W6eITwtlGw60YXNhnNdeSh6bPryEMi3ByROcQR4oRbKnFMTmMsF4EDgh0jVbxsDDGv6t5cqcNBt5fpypQGdTWVO+8c3zanEdkk3JKiffPNY59okNmhQ2OvaKDZ3Lm8YJP/hINe/xpKqYtHCN9ZwaZbFHWjC5uMljTykAinUZj6P1kanTnEIpU4sbkoAgcEO3batNobYl4994vnqvPS8vuWjzDW4SABJqFzLTTojO5A0j6rhD5KePjw+Hk02TD/aLQ6rdcNeNO3ywnPUEpdPEL4zgo2N7qwyWhJIw+J8Gu/de3owBjqCHGKlVTiNOWBxLYicECwJVKjV59Dzavzvnre6NykR4rX4dC3uX0IolHjJJx0Lu9STBE2l82+9IQtJM4f+5j6/9u7+livijN9U2qMsbutrVWS1cYgtVZM2P2nMbf7hzGmjTXd2FASEwyBEq+lYZdlwy5WSTGYVhaDMcUisSrC3txee1dcCoIC5TZGRV0xLK5KJESsGwhiiV1xEQVn857fncPcuVLwEsgAAB20SURBVHPmzMyZOWfmnXeSX87XfL3P+5x5fuec+WDr1jHGe6irvmFDWshL9bpczDemfZU/fNRPKdjwj8amd6GuIqn2PATAFwwtKG4K6JWZaghFnLbxQGEHCXbbtKktL1VeLd+8vGibBjYMFDaq7OBP2NCe2wQQR9WTrkkeokiL+3VpYbIWiA+6Iwd6wj6LiFKwbXoXns2qtycSJ+Wehzt+v6O4IeCVOPTKTDWI/kjVBqg3CjtIsKOjYKq8Wv/C+rJ9OvnJSeX9sWhRTwT5t2IR/FmzeteOHhXPMgadwUA4b7tt/HlfR/BEDfkfOzY+x9/9rnf+F78Yfx6OoG8UpFEN+ZoYO44zoXilFGzT3oUqaHhFU+95+NDGh8obQl4sXmV3rOe4P2Ktn2m9UNhBgm3q7tbipcqr0f2jZfsEHWJVdqxe3RM66GUtB5igBERwxQpWDOmC6yDsfMax4bOTqMlJGx3zOsG85vA9G56eX331bKezTZsmZs97iUPaVILKHz7qrhRs096Fqgrwiqbe8/CBkQfKGwJujlQD90eq9ef1RmEHCTZ3ZzTbVHkl9hSH9kllx969PVEe7PVLG4c5PLXyntkg3OLv9tsZO316XPTy+viz9kdHjvS+W4vl8X24PU6c+GhCphs29OoHwp5KUPnDR92Vgs2/fbgUIFc01Z6Hd667sxRseOWUapD9QXZ0iAAJdofgq4tO9f6ANomPYIFPdlV2wKvtquFQINowVze8poYOahAXnqxhXnE5cFGVz7sc//GPjC1d2vtODt/KYe7y0bFnIpUdUP9bb3Upqbs0Kjt81EYp2FW9C7nT5K1YEVVFU+x5OPCrgeKGgN6YKQeVP1K0B4UdJNjRUS9lXkGHMxBt6IBWZceOHb2n06YrXsETdxvDqmQ7YIw26E1qy2zKdvgivlKw+RO23LtQFmp+bFIZiJtSz8Mf3PuD4mZYtmmZiXnRxglFnLYNRmEHCXbbtKktL2VeiT3FdXbAJ07ol9QkQKcwWDs7dJDteOCBtDqbcXxkO/j5plulYOt6F+oKxNLzEObn7b+rvxDslHuIg69CEUfHgxDXUNhBgh2CGo3yTJlXYk/x7b/fXokDn7ESvh+7hjvv7PXWdk1vmk70B9QXHh6bvh0wLdtnPNEOn/kqBZv35FP1LtQVjqXn4Z539pSCnXIPcfBVKOLoeBDiGgo7SLBDUKNRninzSuwpft/wfVoc4JUy9AiPPYj+gCFeqb0K5/iKdvBzPrZKwdb1LtQVGmvPQ/nVPthQ1fNwdHSU/WTJT9jXrvsau2bBNWzrf23VmRz9tVDEadtwFHaQYLdNm9ryUuYVLE7U/w/97KqbrmLfmfkdtmPHDvapqsdYLQrxREjZHyKKoexQCjYUrOtdKFZM3v/Tn05H1/NQriMcyz0PYVnQyy67kn31q1ezy6cuZFO//s/syxf9DfurSy5nKS8ZGoo4KkxDnkNhBwl2SIo45Z0qr3h79RdfmsqmXP737OtX/Au79NK/ZZdeOpXaKycm+E0UileVgu3au/D55583trytnodyheSeh0D+88//Evv2t3eU4w15h7r+/lH2xS9OTvYmCEUcGdPQx9HZAZPtn3MOY319ve22bfUQkGDXY9RyjOh4ZWA/tVcGIHUcJRSvKgUb7HXpXWhT0bZ6Hsq+k3sewpO1SqxF0YZ/rh/C1DyJBRt/xGxadHaAWHORhi0c1wUS7DqEWr8eHa8MEKD2ygCkjqOE4pVWsF16F9pUtK2eh6Lv5J6H8M364ov/esKTNRdrvoXXTZs3bxazSmLfxh8xGxSdHfBkLQb5WLzG90mwORLRbKPjVQ0y1F7VABTJ5VC8klqdidba9i4MVdGJNXM7I/c8vOeee9jUqf9YK9jf+Mbt7G5YLDaxELs/TOGMzg5ZoOVjlWEk2CpUOj0XHa9q0KD2qgagSC6H4lUfZKz7vfnmm+y9997TxtGlj+3asWPHGNjE6zUwMMCmTl1YK9hXXLGEzZs3r0zH09NWz59U8am678Gez2DYwdgr8dOnT7PP9u1j7Lzz2JkzZ7T8ODRnTvHN++05c7TxUsWM6h3+XqD2KjzGMfO49gm7quGqOg/GphToFVMa3mqdV/DErPpxuPh364suYgxe20yfzq9Ub+kJuxqbjq60zquGdlJ71RDAlpKH4lX2gg3+o04cLbG4QTGhboAGVTqbdNWq3rqEZ8+o90iw1bh0eDZqXlXgQu1VBTARnQ7FKxJsxoohW1/5yiXsmmvUw7ouvjjdsY2hiNP2vRGtHdAzc9q03mLCdaCQYNch1Pr1aHmlQQKGdVF7pQEogkuheEWCPeZcuAkuufRy9pdfvpImIoiA8HIVQt0AcjnGx2fOMDY0xNiUKYzBpAUmgQTbBKVW40THK0Prob2CoaYwwkWc6OkSmujJEMGw0ULxigRb8Nvut3YX05F+8+++yb4787vFMK4Ux14LJhWdm8TjVPdD3QDOeEyaxFh/P2M2E+6TYDvDHSphdLyyMPTkyZPFdKS3/tOtxVTK37rtW2zzK+kNPRVNTtkfbdhBgi2g/NyB54oVumCN2brJ9IVkUe/SDRCRe0iwI3JGryoY7o/dB3eXixXBgiApBwz+APxD2UGCLbB78MXBUrB1y9UJSaLfDUWctg1HYQcJdtu0qS0PA69OfnKyFGxaDrjW5a1ECMUrEmzBfSu2rSgEe+66ucH+IQnFtbIbijitVF4oBIUdJNiCR+PYRcErxtj3//X7Rdu1fPPyOIB1rAUWf4SygwRbINaCoQUF6ZdtWkaCLeASw26oG6BV20iwW4XbpDAUvGKM/Wj1j4q2a2DDgInZ0cbB4o9QdpBgj1H31KenCsLD92t4rRQK8LbvFLKjbcQ15ZFga8Dp5hKW++Onj/60bL/gFXmqAYs/QtlBgj3G7D3v7CkJ/8x/P0OCHdkdH+oGaNVMEuxW4TYpDAWvGGP3P35/2X7tfGOnielRxsHij1B2kGCP0VbsIQ49LUMB3vZdQna0jbimPBJsDTjdXMJyf6z59zWlYKfcUxyLP0LZQYI91k6IPcThlVIowNtulsiOthHXlEeCrQGnm0tY7g8Y1QKf8/gnvW7QbF4qFn+EsoMEe4xjK59eWZAdeohDCAV4c0rb5UB22OEVNDYJdlB4XTLHdH9AhzMQ7J8/9XMXKKJIg8kfIQAlwR5DlfcQX/rk0uIMEScE3dzzROEPEmx3AgRKiYJXYw8YMKQLBHv+4PxAaIXPFpM/QqBFgs0YO33mdEF0IPvaP6wtcCbihKCbe54o/EGC7U6AQClR8GpMsGF0C7Rh8INRLykGTP4IgT8JNmNs77t7S6Jv2belwJmIE4Ju7nmi8AcJtjsBAqVEwasxwYbRLVywYbrSFAMmf4TAnwSbMSb2EOdDIog4IejmnicKf5BguxMgUEoUvBoTbBBpLti8HQsEW7BsMfkjBEgk2Iyx4ZeHS6If/+h4gTMRJwTd3PNE4Q8SbHcCBEqJgldjgn3i4xNlOwajXlIMmPwRAn8SbMbYqu2rCqLPenhWiTERp4Qiih0U/iDBjoJLYiVQ8GpMsMEuGOUCT9mwLkKKAZs/fPuABJsxtujxRQXJlzyxpMSXiFNCEcUOCn+QYEfBJbESKHglCDaMcgHBhlEvKQZs/vDtAxJsxtjMtTMLkq8ZXVPiS8QpoYhiB4U/SLCj4JJYCRS8EgQbRrmAYM94cEYx+kW0NYV9bP7wjXn2gr3/yP6C4EBy3kMcQCbi+KZas/xQ+IMEuxkJAqRGwSuhvdr62tayPYP1EVIL2PzhG//sBVvVQxxAJuL4plqz/FD4gwS7GQkCpEbBK6G9EtszGOaVWsDmD9/4Zy/YG1/dWP4jPfT+oRJfIk4JRRQ7KPxBgh0Fl8RKoOCVINh//r8/l+0ZjH5JLWDzh2/8sxfs1btWFwSHHuIw4xkPRByORBxbFP4gwY6DTEItUPBKEGwwjU+zDOsjpBYw+sOnD7IX7MUjiwvBXrZp2ThciTjj4Oj8AIU/SLA755FcARS8kgQbFv+APjnQtqUWMPrDpw+yF2zeQxzm4RUDEUdEo/t9FP4gwe6eSFINUPBKEuz1L6wvBBt6iqc2pzhGf0iUa3SYtWDDrGbwTxR+I6+MjAOSiDMOjs4PUPiDBLtzHskVQMErSbBhWlLerh04ekA2OepjjP7wCXjWgi32qIThEGIg4ohodL+Pwh8k2N0TSaoBCl5Jgi22a6n1FMfoD4lyjQ6zFuxNezdV/hMl4jTilffEKPxBgu2dF00zRMErSbAPf3C4bNfkN4dN8QqdHqM/fGKWtWDzWYHgO7bYQxwAJuL4pFnzvFD4gwS7ORE854CCV4r2ivfNgVEwKQWs/vDlg6wFG+YOh289C4cXTsCTiDMBkk5PoPAHCXanHFIVjoJXCsHmo19gnYSUAlZ/+PJB1oI9+5HZhWCrVrYh4viimJ98UPiDBNsPGTzmgoJXCsHmKxDe/NDNHtEKnxVWf/hCLlvBFnuIq2YEIuL4opiffFD4gwTbDxk85oKCVwrBFmdwhG/aqQSs/vCFf7aCLfakHN0/OgFPIs4ESDo9gcIfJNidckhVOApeKQR798HdZcczeQSMCodYzmH1hy98sxVsGO7AxyqqVrUh4viimJ98UPiDBNsPGTzmgoJXCsGuWoXQI3RBssLqD19gZSvYMLMZCPZNv7pJORsQEccXxfzkg8IfJNh+yOAxFxS8Ugg2jHqBmc6gjYPRMKkErP7whX+2gr188/KCzPMH5yuxJOIoYensJAp/kGB3xp+qglHwSiHYYC9fBGTpk0urzI/uPGZ/+AA7W8Ge99i8QrBVPcQBWCKOD3r5ywOFP0iw/RHCU04oeFXRXsFqXfCEDaNhUgmY/eHDB1kK9slPThZEBjLDRPmqQMRRodLdORT+IMHujkAVJaPgVYVgD700VLZz0OalEDD7wwf+WQq22INS1UMcgCXi+KCXvzxQ+IME2x8hPOWEglcV7ZU4EiaVOcUx+8MHZbMUbBBpeLqG37NvPavEkYijhKWzkyj8QYLdGX+qCkbBqwrBhtEvvJ3bsm9LFQRRncfsDx9AZynYgy8OlkSuelVExPFBL395oPAHCbY/QnjKCQWvKgQb1sLmgg1tXgoBsz984J+lYPPOGHPXza3EkIhTCU0nF1D4gwS7E+7oCkXBqwrBBrsHNgwUog2jYlII2P3R1AdZCrbJcAciTlNq+U3fmT927WJs+vSJxjz1FGPnnMNYX19vu23bxDjyGRJsGZHOjzvjlWfLq+zgw1dhVEwKocqOFOou1jGUHdkJtumEAqEAF53axj7Z0RDladN6oixnA2LNRRq2cFwXSLDrEGr9Ovb7g08QBZOoyEsItw62QYHY/WEAgTZKdoJtOmUfEUfLm9YvduoPeIqWg3xOPpbjwzEJtgqVTs91yiuPllfZUTcFs8cqeMmqyg4vmbeYSSg7FC1RM6tCVbRZrc6mFod06YY6xG7HWYv0e2SHHh+jqyoxls/Jx6qMSbBVqHR6Dvv9IQ7tqhrC2qkDpMKx+0My1/qwDwDK6Xf3v93N+u/qL34jW0eysj0nP5vYWnW3iGmLOGNizM/L5+RjHk/eHpozp3i9/vacOcS7zNodmQttHW/evrls73722M+Id4nzLrsn7NW7Vhe9JmFhd903HbihMASyQ+NFEGLVT06ienqWz8nHch5wTE/YKlQ6PZfD/THr4VlFm7dq+6pOsTYpPAd/mOBQFSc7wV48srgg76LHF1VhUpwn4mjhaf1ip/5QibF8Tj5WIUSCrUKl03Od8sqj5To7ljyxxKjN81gd56x0djhn2kHCUHZkJ9jwZA2TCdT92wwFeNvcITs8IK4SY/mcfKwqlgRbhUqn53K4P/hbxZlrZ2rfKnbqiLHCc/BHE5yzEuzjHx0vxBoEe/jlYS1uRBwtPK1f7MwfH37Ye20OWzHQsC4RjWT3O+OVZ8R0dmx8dWPZ7r17/F3PJfvNTmeH35LC5hbKjqwEW+wxufONnVqPhQJcW2iAi2RHQ1DhyZn/xKz42Gu4BuINE6nUBXrCrkOo9es53B/iyJitr21tHWObAnPwhw0ectysBFsck7jvf/bJWIw7JuKMg6PzAxT+IMHunEdyBVDwSjM1Kdh78L2D5RP2yCsjMgRRHefgjyaAZyXYfNYfeCUOE+PrAhFHh07711D4gwS7feLUlIiCVzWCDaNh4Ps1tHtrRtfUINLt5Rz80QThrAR76ZNLC9KazKtLxGlCK/9pUfiDBNs/MRrmiIJXNYINEM0fnF+0fQuHFzZELGzyXPzhimJWgg1CDf8yl21aVosXEacWolYjoPAHCXarnDEpDAWvDAQb2jxo+2BMdswhF3+4+iAbwYZ1r4Gw8INX43WBiFOHULvXUfiDBLtd0hiUhoJXBoI99NJQ2f7BaJlYQy7+cMU/G8EWe0pu2rupFi8iTi1ErUZA4Q8S7FY5Y1IYCl4ZCDbMI84fWOpGyJjgFipOLv5wxS8bwX72rWdLwsJ+XSDi1CHU7nUU/iDBbpc0BqWh4JWBYIsPLCTYBsRoGCUUr7IRbPGV0ImPT9S6IxTgtQV7jkB2eAa0SXYk2E3QC5I2l/tD/CS4/oX1QbD0kWku/nDFKhvBXvn0yuIJ27TTBRHHlVJh0qHwBwl2GHI0yBUFrwyesAGiBUMLijZwxbYVDRALmzQnf7ggmY1gw3AG+IYDE+GbBCKOCUrtxUHhDxLs9ghjWBIKXhkKNh/WCkO8Yg05+cPFB9kItu3EAUQcFzqFS4PCHyTY4QjimDMKXhkKNp84asaDM6JdBCQnf7hQNgvBhgnveQ9Jkx7iACQRx4VO4dKg8AcJdjiCOOaMgleG7RV0NuPt4P4j+x0RC5ssJ3+4IJmFYIs9JE0nvyfiuNApXBoU/iDBDkcQx5xR8MpQsMWRMrCuQowhJ3+44J+FYG/Zt6X8Z3ng6AEjnIg4RjC1FgmFP0iwW+OLaUEoeGUo2Ic/OFy2g7DkZowhJ3+44J+FYK/9w9qCqDbfbog4LnQKlwaFP0iwwxHEMWcUvDIUbICI9+VZvWu1I2Jhk+XmD1s0sxBs3jsShjWYBiKOKVLtxEPhDxLsdshiUQoKXlkI9qLHFxUPL6ajZSyg9BI1N3/YgpaFYM9dN7cgqc34QyKOLZXCxkfhDxLssCRxyB0FrywEe9X2VUVbaDofhQOkjZLk5g9bsNALtjjDz+CLg8b4EHGMoWolIgp/kGC3whWbQlDwykKwh18eLgQbeoubzPhog6WPuLn5wxYz9IIt9hCHCfBNAxHHFKl24qHwBwl2O2SxKAUFrywE+7kDz5WCHWNP8dz8YUHVIip6wRaHMgBZTQMRxxSpduKh8AcJdjtksSgFBa8sBHvPO3tKwY5xEZDc/GFB1SIqesEWF/2A1+OmgYhjilQ78VD4gwS7HbJYlIKCVxaCLX4ijHERkNz8YUHVIip6weaLfkDHM5tAxLFBK3xcFP4gwQ5PFMsSUPDKQrABnnmPzSuesm064VrC6hw9R3/YgIVesG0X/eDgEXE4EnFsUfiDBDsOMgm1QMErS8FetmlZIdgxLgKSoz8EOtbuohdsPlEATJ5iE4g4NmiFj4vCH46CDba38bPxIgp/WAqdDT5tx7Xxh8tEUm3ZY2NHW3VyKSeUHagFW1z0Y+SVESvcQwFuVQkPkckODyD6yoIE2xeS3vLJ8f6A9RRiXQQkR3/YkBm1YItDumyHMBBxbGgUPi4KfzQU7FAoA7a2+NrGD1X3pvnmaEfMQ7ty9IcNh1ELtrjox8H3DtrgYt2AWWXeYmS6AVoEu64oEuw6hFq/nuP9cfR/j5ZP2LEtApKjP2xIj1qwm3yrIeLY0Ch8XBT+IMEOTxTLElDwyuFbPO/bE9siILn6w5S2qAXbZdEPDhwRhyMRxxaFP0iw4yCTUAsUvHIQ7FgXAcnVHwIltbuoBdtl0Q+OFhGHIxHHNjl/XH01Y319Zr8LL9SCDLaHtN8l/5D10YLh+WKudsS6CEiu/jClNVrBFmf0sVn0gwNHxOFIxLFNzh8//rGZWIOo33yzFmSwPaT9LvmHrI8WDM8Xc7Uj1kVAcvWHKa3RCrbYQ9xm0Q8OHBGHIxHHNjl/jIyYC/bq1VqQwfaQ9rvkH7I+WjA8X8zVjlh7iufqD1NaoxVsEGk+1hAWALENRBxbxMLGT84fR44w9vnPm4n2a69pwQPbuf2vv/46mzRpEuvr62PTp09nZ86cUaaF83Ad4kF8SAf7/CcmEvMXz+v2eX10cVK4lqsd4iIgtkNeQ/o1V3+YYopWsGGiFC7YNot+cOCIOByJOLZJ+uPKK+sFe/Jkxj79VAsy2C7av3Tp0lJ4V6xYoUx77733lnHuuOOOIg4Xa9iKQc5fvFa1L9anKk4K53O1Q/xkGNMiILn6w/ReGX/nmqbSxIsF8Pt33l8Itu2iH9y0WOzg9XHdkh2uyHlIt2BBvWD/8Ie1BYEPRT+eOnWKTZkypRDk888/nx08OH6OgUOHDrHzzjuvuH7ZZZexkyd7q9Sde+65xTnYikHOX7xWtS/WpypOCudztgPmEoeHmpgWAcnZHyb3C1rBXjyyuCAjTHTvEog4LqiFS5OkP0y+Y9d8vwZEwXbZ/h07dpRP0DfeeOM44G+44Yby2jPPPFNeu+6664rz/f395bmq/MdFUBzI9VFESeJUznbwRUCgrYwl5OwPEx+gFWw+McCjzz1qgsOEOEScCZB0eiJJf5h8x37zzVpcwXaV/bNnzy6FeWhoqMhneHi4PHfLLbeMy3tgYKC4BunEUJW/GEfeV9VHjpPCcc52wKtweMKe8eAMdurTU1G4K2d/mDgApWAf/+h4QUQgo+2iHxw0Ig5HIo5tsv7Qjcc2+H4N6IPtKvvff/99duGFFxYiPHny5OLVOGzhG/UFF1zA4LpJqMpfl1ZVH138WK/lbMfON3aW7eSBoweicFHO/jBxAErBfvntl0siwnziLoGI44JauDTJ+kP3Hdvg+zUgCrZX2T84OFg+UXOxBsHesGGDsTN0+VdlUlWfqvixns/ZDnEkDYh3DCFnf5jgj1KwxeXjXP85EnFM6NNenGT98ZvfVHc8e/BBIwDBdp39119/fSnaINbXXnutUb48Ul3+PJ641dVHjBf7fs52HP7gcOMHG9/+zdkfJliiFOxfP/vrgojwbeb0mdMmOEyIQ8SZAEmnJzrzx65djE2frrZdd42nOHasWrBrxl/zLMB2nf3QSxyEmv8OHLB7vVmXP6+HuNXVR4wX+37udvC+PmtG10Thqtz9UecElIK9fPPyQrBh2IJrIOK4IhcmXWf+mDatJ7gqs3TXxPiq79g184eLycH2Ovu5WMPWNpjkL+dZVx85fqzHuduxcHhh0VbCQkkxhNz9UecD+7u7JscYAB/YMFCQsMn4whjsqIHa6DLZYQSTPpJOBHXXeK6qecVr5g/nSWELPqzzIwm2iJj5fh2u5jl1G9PVjpVPryzaStf5Knxb7WqH73o0zS+UHegEG4Yn8BnOmszgEwrwpkSwTU922CKmiK8TZd01npVqPLbB+GueHHxY50cSbI6W3bYOV7vcuovtasfQS0Nle+kyI6Rvi13t8F2PpvmFsqMPMsb0e+Q/HmH9d/UXv/uG70NlGyY/xWBL1U0p1q2IMybK4nnY110T476wcSP7bNKkcd+y/3PdOq/cFAVbLJv2cbVvvv35y9/+smwvYd93/pSfX/6he8IWV6FpMlQBiIYhkB0aL4IQq35yEt1TtO6amI84r/gXvlA7f7iYlDd64jl5XxRs+VrdsUn+ch7EKxmRbo9d/dF0VUPfVrva4bseTfMLZQc6wRYX/YAJVFxDKMBd6+OajuxwRU5IpxNl3TUhCyaOx77qKvFK7T74sM6PJNi1MCoj1OGqTBThSVc7Tnx8onwlDq/Huw6udnRdb7n8UHagE2y+6Mesh2fJGFodhwLcqhIeIpMdHkDUibLumli0+B37e98Tr9Tugw9D+tEl/5D1qQXEYwSyg7HZj8wuRBs6oHUdyB96D6AT7CVPLCnI13RCeyKOnjhtX+3MHx9+2HttDls56K7JcWFe8c99rpcXPG1bBLA9pP0u+YesjwU0jaOSHYzdsfGOos1c9Piixng2zYD8oUfw/wHQERyKxAIpWQAAAABJRU5ErkJggg==[/img][br][br]3. (e) Draw graph of [math] y = x^3 [/math] [br]Solution:[br]Given, [math] y = x^3 [/math][br]Now, [math] \begin{tabular} {|c|c|c|c|c|c|c|c|c| } \hline [br]x&-3&-2&-1&0&1&2&3 \\ \hline [br]y& - 27 & - 8 & - 1 & 0 & 1 & 8 & 27 \\ \hline \end{tabular} [/math][br][img]data:image/png;base64,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[/img][br][br]4. Pemba estimates the minimum ideal weight of a woman, in pounds is to multiply her height, in inches by 4 and subtract 130. Let y = minimum ideal weight and x = height.[br][br](a) Express y as a linear function of x.[br][br]Solution:[br][math] y = 4x - 130 ...(i) [/math][br][br](b) Find the minimum ideal weight of a woman whose height is 62 inches.[br]Solution:[br]Here,[br] [math] \begin{align}[br]\ & y = 4x - 130...(i) \\[br]\text{Putting } x = 62 \text{ in equation(i), we get,}\\[br]\ & y = 4\times 62 - 130 \\[br] \ & or, y = 248 - 130 \\[br]\ & \therefore y = 118 \text{ pounds.} \end{align} [/math][br][br](c) Draw the graph of height and weight[br]Solution:[br]Here,[br]We have, [math] y = 4x - 130 [/math][br][math] \begin{tabular} {|c|c|c|c|c|} \hline [br]x&0 & 5 & 20& 40 \\ \hline [br]y& -130& -110 & -50 & 30 \\ \hline \end{tabular} [/math][br][img]data:image/png;base64,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[/img][br][br]5. Investigate the nature of graph showing linear, quadratic and cubic function in our daily life. Make a report and present it in classroom.[br]
– AMBIK BARAL

1.2.

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1.3.

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1.4.

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2.

Polynomial

  • 1. Unit 1.2.1: Polynomial
  • 2. Unit: 1.2.2 : Synthetic Division
  • 3. Unit 1.2.3(A): Some theorems on polynomials
  • 4. Unit 1.2.3 (B) : Factor theorem

2.1.

Unit 1.2.1: Polynomial

Exercise 1.2.1
1. (a) Define polynomial of one variable.[br]Solution:[br]A polynomial in one variable is any expression of the type [br][math] a_nx^n + a_{n-1} x^{n-1} + … + a_2x^2 + a_1x+a_0, [/math][br]where [math] n [/math] is non-negative integer and [math] a_n, a_{n-1} … a_0 [/math] are real numbers, called coefficients. [math] a_nx^n [/math] is called the leading term of the polynomial. [math] 'n' [/math] is degree of the polynomial. [br][br](b) If [math] p(x), q(x), d(x) [/math] and [math] r(x) [/math] represent polynomial, quotient, divisor and remainder respectively. Write the relation among them.[br]Solution:[br]We know, Polynomial = Divisor x Quotient + Remainder[br][math] \therefore p(x) = d(x) \times q(x) + r(x) [/math] [br][br]2. Divide using long division method and find quotient and remainder in each of the following:[br][br](a) [math] x^2 - 10x + 21 \div (x-3) [/math] [br]Solution:[br][img]data:image/png;base64,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[/img][br]Quotient [math] Q(x) = x- 7 [/math] and remainder [math] (R) = 0 [/math] [br][br](b) [math] x^3 + 2x^2 -5x-6 \div (x+1) [/math] [br]Solution:[br][img]data:image/png;base64,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[/img][br]Quotient [math] Q(x) = x^2 + x -6 [/math] and Remainder [math] (R) = 0 [/math][br][br](c) [math] x^3 - 8 \div (x-2) [/math] [br]Solution:[br][img]data:image/png;base64,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[/img][br]Quotient [math] Q(x) = x^2 + 2x + 4 [/math] and Remainder [math] R = 0 [/math] [br][br](d) [math] x^3+9x^2+27x+27 \div (x+3) [/math] [br]Solution:[br][img]data:image/png;base64,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[/img][br]Quotient [math] Q(x) = x^2+6x+9 [/math] Remainder [math] (R) = 0 [/math][br][br]3. Divide using long division method and find quotient and remainder.[br][br](a) [math] x^3 + 2x^2 -5x -7 \div (x+1) [/math] [br]Solution:[br][img]data:image/png;base64,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[/img][br]Quotient [math] Q(x) = x^2 + x - 6 [/math] and Remainder [math] (R) = - 1 [/math] [br][br](b) [math] x^3 - 10x^2 + 16x + 26 \div (x-5) [/math] [br]Solution:[br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOIAAADmCAYAAADIgVnBAAAdFklEQVR4Ae2df4RW2R/HI8nKWrHa9MdKjKxkjUh/9MdK/2Q3lUSS0daIZGVsozVWJTZppMaoDCu1VlKSpJJNrSRJmW2SJiMym1QSSVZWztfrrvN8z3PneZ45zz3n3nvOM58P97k/nnvP+Zz3Oe/7Off8+JxJSiQXBJ4/f67Onj2rPn78qLq6ulR/f38u8UigrYHApNZIRnip+O2331R3d3ei2Lt379TMmTPDU1I0CgYBIWJOWfHmzRs1MjKShP7o0SO1aNGinGKSYFsBASFiAbm4efNmNTg46D2m48ePq+XLl6stW7aozs5OtW7dOvXhwwfv8YwX4KtXr9S2bdsU+uzdu1ddvHhxvEfk/xQCQsQUIL5PT548qe7cueM72CS8X3/9Va1du1atXr1a7d69W2GFy5D29vaqNC5evLhSGyhDnxjjFCLmmGs3btxQjx8/TmLg2LdAxLLl2rVravLkyVVqbNy4UfX09FRdk5PGCAgRG+PT8N/z58+rgYEB9eDBA3X//n117tw5RcFEsIIzZsxQs2bNSjYsl2+BiLTKXrlypcoi6Xga6afvcd2fPn1aTZ06tSqYrVu3JlXmqoty0hABIWJDeOr/SZWT1lBk9uzZigJ56tQp1dbWVv8hz/9ARFpn+S7E4q5ataoSQ1H68QKaNGlS8kLQkXd0dBSKg4435r0QMUPuYYX++OOP5Ml///03sQhce/v2rXr27FmGELM9kv4mpOHm6NGjCSmK1I8XANYX4eW0Zs0aNXfu3GyJmqBPCREdM54Cv3Tp0syhYNGoyjXaqPrWkidPnlRd3rBhQ0IC86Ktfi568DLq6+tLBjBASFpxTets6iPHtREQItbGxfoqrZV79uyp3M+ImiLk5s2bSZWQqqEWqoTpb9Ey9MMiHjhwQKslewsEhIgWIKVvuXXrlurt7U0u01R/4cKF5Pjhw4e59Bem4+ecajAkMwVd+DYsWj8apGgwQqiaUi3V38+mfnJcHwEhYn1s6v5z8OBBhfWhOnf48GH1888/q8uXLycNNnUfyuEPxrLSUvv+/fukI33Hjh1JLEXrx0ACyP/06dNkYIFppXNIdksGKUTMmK288fk2Qmi1xEKVIXwnYpHT34tF6qcbrxhRozEpA4uY4xQixpx7onvLICBEbJmslITEjIAQMebcE91bBgEhYstkpSQkZgSEiDHnnujeMggIEVsmKyUhMSMgRIw590T3lkFAiNgyWSkJiRmBYIlIJzEdxGfOnFHff/+9+umnn5LJpkw4TW/79+9Xhw4dyrSdOHEiGRbG0LBmN3S7evVq5o2pS0NDQ01vf//9t3r58uW4W3p2RswFtdV1D5aIAM98O+a6sX3xxRfqu+++SyacMt1HNr8Y4G5j06ZNTW3Mski/FJs537VrV6aXp37pHjlypOmXp/myzfIivXfv3pgX5/DwsPN7ImgikrpffvmlQkYGE9fKaApEs4VI308BFFL7JfVExFN77MvKyOCJSMIYVKwt448//pg1rd6fY4ypTRWx3j1UMbNUTanS2lSJL126ZG0xqKJrS2O755Og1ovR9tr27dszv0B5kXZ0dATzEnW1ilEQkQHVX375ZYWMVC9EBAFXBLK8SCFc+uXpag1JRxRERFFmGGir+Omnn46ZbeCaKfK8IFAmAtEQEZBWrFhRIeOSJUvKxE3iFgS8IhAVEZlzhw9NbRmliuq1LEhgJSIQFRHBCff1moi4MaS/UUQQiB2B6IiI52xNRPYheLuOvRCI/uUjEB0RgYzvQ03GefPmlY+iaCAIOCIQJRFZdUgTkX0e60o44iqPCwJNIRAlERlDaRKRRU9EBIGYEYiSiAC+YMGCChmnTZtWaKMNHtIYkB6j20AGR+CNm8VTRcJBIFoi/vDDDxUiYh31Kkx5Q0tB1p698WaND9FYBC/k+EKlpbmrq0v19/fHonrL6xktEVl9yayeMr6xCKEvk9VxESwL7uVjERwid3d3J+pi1WfOnBmL6i2vZ7REHB0drSJi0SNtsCosHHP37t1oCgnf1npcJFXTRYsWRaN7qytaOhFd1oFngUxtFdOLZeaZcQwWZuwr68XnRUT6S7Fe6dFDkAnrTxUTd//sswgDIwYHB7M8Ou4z9XTXD96+fTtZpoD1JKnav3jxQv9V2J4X0b59+5JVrJi2xYKzaSlSz9KJSId81nXgWQ5NE5E9BSBvwRJqt/LEx6wQ30J3DESngFCdNIXlzsyGFs5Z/KYZgdysaGwrLO32zz//WN3eSHcC4MXFmGEt8+fPV8eOHdOnTntbPck/SKiFajoL6fC5oyVPPXUc5j4IIpoKNXO8fv36KiKyIEveghXs7OxMouFNTottXgLJTCISHzNPTOFFRsOVrUAU/cKy7X8lDgprM5LWXT/b3t5eWTmKaxT4V69e6b+d9rZ6QljGLGPxtGAMzCXt8tRTx2nu6xKRhoh668ObAbgeAx5Wpt468I3CZ/Uj0yJSzfUhjdJOIebNiYVgFSj0z0vShZkXTbqBherdN998U6VCPf2xgjNmzEje/lgAs+BVBZA6sS3g5mNp3fkPS05+gR1pQU/y3pR6upv31Du21ZP4d+7cqV6/fl0JikY3JqAjNnpWHvR0UJOIVF30GzDv9eEBj7c+3128oclAW0mPsKHxxFVs0k7hQde8nTOlC/Pvv/8+Zm16vhE///zzSrJt9K/cbHlgW8DN4NK68x/kmzJlSvIiA0Ma3JYtW1ZZSctV9yx6ohdlnZqNtpDj6Wmm09fxGCICEKYboS5NIwjX6D/LY334dGHmu4h14G2EQmhaRFwnuEjRaR9P13Rh5oWVXpseDKZPn54ElZf+WQp4WncUxHqnv+VZbpxGKR+6Z9ETvfB5RMOXlkZ66nt878cQ0YwAQtqsD08BabQGPP+5rANv6mQem7P2yWCffXq2aTf1MY9dMNHhpAszVeJaVdOvvvpKP1LZZ9Wfly/fnGZ+0jVEK6t5jULfSNK6cy/VTvLJFEjIKClTbHT3pSeDGtJpsdXT1Nn1uBqVVGh5r79uuw58Sq3KKav0mhaRzPcleafdRs90YaZh47PPPqt6lOp5rReQT/2zWJq07iit+36xfloYHLFw4UJ9muyz6t6sngxTZNOiq6a2eurnfOzHELHI9dep7gK6KXodePNavWPenCYRqda6SJFpt9GzVmFua2ur+jZlwDtVKSQv/Zst4OhSS3euY/3M/ktavmn08qF7M3ryjU+1ngYbNs4Zsqilnp76f9/7MUQsev11wODjOL0OvE1C00T89ttvbR6re0/Raa+nCIWit7dXzZkzJ5l7Ses1b2mEWgTjRKmaUaDNrou89G+2gNfTHf0ZKE9rLe0N1GjwK0srpg/dbfVkmCLf1eZLnGP9QmukZ5IJOfyMISJx0IpERiO0ZmK58hSA4XuPfTOSrpqaHcXNhGPeW3Tazbhtj8kPvmNqzf7IQ3/bAm6rPzqS3+lBBa66F6WnbTqbua8mEZsJoMx7qd+bbzXeriL+EfDV4e5fs+oQY9GzWuv/zqImIlVak4i6Q7ZWQuWaIBAyAlETkQ5gk4h66FnIgItugkAtBKImIh3/JhHNgby1EivXBIFQEYiaiFhAk4hmq1eogItegkAtBKImIn1VJhHpzhARBGJEIGoiMpfNJCJdLSKCQIwIREtEhkmZ62AwS6QIoa8rZA9uuo/RnDxcBC4ShxsC0RKRcYGmNWSoVN5CIQ/Zg5t4acu7BOQXfrRETLeY+nK30Ajq0D24MeNDvLQ1ysFw/4uWiIyiMS1iHnMl62Ub1WKmBDEbIiQRL20h5UZzukRJRIjAjGpNRPyLFCV5e3Bz8WpnYpCnlzYzHjn2g0CUREzPumC0fxHCC0APhs/LgxsDl5mdgMVniljag4FNOhlxlB5QbfOc3FMeAlES0ezIp+W0KL+YRXhwg4guwhSqZr20ucQnz/pBIDoiMm/xk08+qVRLa81Od4GmkRexIjy4QUQsbz2vdo30y+qlzQUvedYPAtERkVnU+tuQvc8GExsvYpAEq5OlymiTZRCR1s9aXu1s9LOJQ+4JD4GoiMj3GZ61NRFdXWOY2QHB9BA54snbe50Zt3mcJrj2aheKfqaucuwPgaiIaFpDvg2bdTVvCxuEtPFeVy88Fw9uaS8FuBtMV79d9aunt1wvD4FoiIiDH9PPCA6H8pKsXsRc9bH1aleWfq7pk+frIxANEbEKukqK+z2qaj7FhxcxV30YQlfPq10I+rmmT56vj0AURDRn4rN2A2MqfYsPL2I+dKrn1S4U/XykUcIYi0DwROQ7kBWQsIbsfbaSpuFw9SKWDi/reT2vdqHolzVd8lx9BIImIl65mN4ECek7/PPPP+unRP4RBCJGIGgi0iDDLHw2+u5EBIFWRSBoIrYq6JIuQSCNgBAxjUiO5/T/4V5eRBBIIyBETCOS4znD12hwEREE0ggIEdOI5HguRMwR3MiDFiIWmIFCxALBjiwqIWKBGSZELBDsyKJqaSK6DL52zUdmcPhYAttVD3k+DgRamoihZYFYxNByJBx9hIgF5oUQsUCwI4tKiFhghgkRCwQ7sqiEiAVmmBCxQLAji0qIWGCGxby0dIEwTciohIgTMtsl0aEhIEQMLUdEn1IRwHvey5cvG24jIyNqaGgo2Tj2IUJEHyiWFAYe38YrNPr/4eHhSuHRhajW/t69e+rq1atW25kzZxTeE2y2I0eOqEOHDo277d+/X/X09FhtW7ZsUZs2bbLa8JyOR7w8Nh9kjIqI5pvILETXr1/3WnBsC82uXbusCgwFy7bQdHR05FJY8iiAEuZ/xJ5QRMR9xMqVK6WQ5vRWz5tUvGBsrBcvLFuLiPW0sbLcc+LECSvLjZUfr0aAR3VtCKhp+JBoLCJvnbwLiw7fttBs377de6HBGttU9bjn0qVL4xYaXaiocurC02hPwdLV2fH2slS6Dwr+F0Y0RERdrGKtQoRXt/EKDf9LwfFXcCQkvwhERUS/SZfQBIFwEBAihpMXoskERkCIOMEyH2/iLO326NGjCZbysJMrRAw7f7xqx7c0nsRZrqCrq0v19/d7DV8Cy46AEDE7dtE9yUTp7u7uRG+cWM2cOTO6NLSqwkLEVs3ZGuliJI7ufKZqumjRohp3yaUyEBAiloG6Q5zHjx9P+lPp+O7s7FTr1q3L1C2zefNmNTg46KBJ/UdZ4hzLS19nWm7fvq3w4H7q1CnFwjovXrxI31LIOS+iffv2qb6+vgTPgYGBqniL1lOIWAV/+CfMaVy7dq1i7CRLuKVXGLZJAQRhdIitNOMYmaURLly4kBRuqsKmsIDQihUrKpfmz5+vjh07Vjl3PbDVE39CkFAL1fRZs2ap06dPJ5fy1lPHa+6FiCYaERxDRBeBKFgsxHY9kSwTmlmvJE3E9vZ2deXKlYr6FHifczRt9YSwrDiN1dPCy40NyVtPHae5FyKaaERwTGGj1ZMCXcuq0TVBNevBgwfq/v376ty5c+ratWtJyrif9SV5+7Ppgjdesm0LuBlOmohUBVnViyUH0Ak9ay0220h/M/xax7Z6osPOnTsVq1BrYSFcqvm2eurnfO2FiL6QLCgcChuWhuF6WDQKvBaqnNqlP8vZUdXiW6ytrU3fkmlvW8DNwNNEhHxTpkxJdIKAo6OjatmyZYp+TS2u+mfRk7jBbNq0aYmFtNFT6+tzL0T0iWYBYaW/CRmofvTo0cS6UOVC+AaaOnVqco2C/uzZMyfNshTwNBF5IWARdbUYhTZs2FDpToGcrvpn0RM9aPg6fPhwgtF4ejoB2eBhIWIDcIr4C+u2devWhhvVTC0MfDeFwky1yhQK9NKlS81L1se+HCOniUiVEyKaQsvqggULzEvJsY3+vvRkUAME1tKMnvoZH/tqZHyEKGHkhsDNmzeTwsy3nxambKW/9WhN3bNnj75FMaLGRbJYmjQRqYpCRPO7cNu2bWrhwoVjVMuqf7N6Xrx4UbFpofGmGT31cz72QkQfKBYUBtVMCqkpixcvTvrrbt26pXp7e5O/uEYXAvLw4UPn/sJmCzjxponINayf2Xe5fv36pE+R/3zo34yefF8z3I8GGzbODxw4gCoN9UxuyOFHiJgDqHkGSeGhQeH9+/dq7969aseOHUl0dI5jHanq8r1Dp/nly5crfWMuOjVbwHkhzJkzRy1ZsiRpwcXKIFhyrDffrOhGX6heuNWH/rZ6Ur2fPn16YqGx0nrj+3A8PZMbcvgRIuYAat5BUpCweOnvRVr/+HZCaFU1WyS1TlzjO4hmeluxLeA24aEjutfqerHRv1EcRenZSIes/wkRsyIX4XNZZ1/47HTPE7ZY9KyFgRCxFioteo1qq8y+CDNzhYhh5ksuWsnsi1xg9RKoENELjMUFEvrsi0azGnzpXhzaxcUkRCwOay8x0SBBy2OIsy9oKGo0q8GH7l5ADDAQIWKAmdJIJQqzi9BfpoeZcWwjtq2RjIhpNKvBVXcbXWO9R4gYWc5RmBmdEuLsi0azGoB5PN25x2X2RWRZWaWuELEKjvBPKMwxzL4ASXNWA+eNdOd/19kX4edefQ2FiPWxCfKfWGZfAJ45q4Hzerrzn4/ZF0FmmKVSQkRLoPK6rVVnX6RnNYBfeiRQrZkj3Gcz+yKv/CgrXCFiWchniDeW2Re1ZjXY6g4sWWdfZIA0mEeEiMFkxfiKxDD7ot6shka6k3Ifsy/GRzDcO4SI4eZNTc1Cnn0x3qyGerqTUB+zL2oCFslFIWIkGWWq6TL7wgzH9pjWTlpAfUg93QnbdfaFD/3KCkOIWBbyEcUb86yGWGAWIsaSU6JnSyMgRGzp7JXExYKAEDHQnKIvTbuRCFRFUcsjAkJEj2D6DMpnA4lPvSSsfBAQIuaDq3OoQkRnCKMKQIgYaHYJEQPNmJzUEiLmBKxrsEJEVwTjel6IGEB++XIf75KUZgefu8Qlz45FQIg4FpMgrohFDCIbClNCiFgY1M1FJERsDq/Y7xYiBpqDQsRAMyYntYSIOQHrGqwQ0RXBuJ4XIgaaXzLQOtCMyUktIWJOwEqwgkAzCAgRm0FL7hUEckJAiJgTsBKsINAMAkLEZtCSewWBnBAQIuYErAQrCDSDwIQn4vDwsBoaGpJNMMhUBig/PmRCExEQly9fLptg4FQGfJBRiCiF0KkQyotsuRIieqgTAKJUTaVqnrUM+CAhxXhCW0QPPJYgBAEvCAgRvcAogQgCbggIEd3wk6cFAS8ICBG9wCiBCAJuCAgR3fCTpwUBLwgIEb3AKIEIAm4ICBHd8JvQTzNnctu2ber48eNq7969igVKy5BHjx6pffv2qb6+vqRPdGBgYIwat2/fVj///LM6depUsgTcixcvxtxT5gUhYpnoRx53e3u7unPnTiUVixcvViMjI5VzlwPbJQfwgAcJtbC026xZs9Tp06f1JXX37l21YsWKyvn8+fPVsWPHKuchHAgRQ8iFCHW4du2amjx5cpXmGzduVD09PVXXsp7YugqBsOiBxdOydu1axaaFF8aVK1f0aULM0DwgCBEr2SMHzSCAxZk6dWrVI1u3bk2qhvri+fPnFdXEBw8eqPv376tz584pCGwjtkRkoZ6dO3eq169fV4Jds2aNWrduXXJOtXXSpEnJgj7Ej04fP36s3BvKgRAxlJyITA+IRQE3C3VHR4dqa2tLUnLy5MnKKsOzZ89Oqop8n+n/x0uuLRHT4VA1nTZtWsVCQr4pU6Yk8aPr6OioWrZsmXr79m360VLPhYilwh935KtWrUosDKmAAFiiuXPnJuSkyojwDYflhAQU/mfPnlklOisRt2zZog4fPlyJA/Lzwnj8+HHl2oYNG1R3d3flPIQDIWIIuRCIDs263YdktFSePXs2ISQkgJymQMilS5eal8Yc+1pyoL+/X0FgU6iKQkRTIOGCBQvMS6UfV2tYujqiQMwIYBEPHDhQlYTdu3erPXv2VK49f/68ctzooFmLSNeJ2X2iG2+oiqar0HS5LFy4sFH0hf8nRCwc8taJkG4C3RpJ1ZRqKftbt26p3t7eJKF0aVy4cCE5fvjwoRocHLQCoBki3rhxI7HKNNiwcW6+ELB+Zrzr169P+hStFCnoJiFiQUC3YjS0TEK6p0+fqs7OzqRllHQePHhQ0XBDVZfvNTrSL1++XNW3Nx4etkR88uSJmj59emL1sHx649tQCw1LdGfwfYoeq1evDm5ZdCGizi3ZN40ADTB8A1Il5DvPFCyjvvbhw4emWyltiWjG2egYfbDM5gCERvcX/Z8QsWjEJT4rBELrcLdS2uEmIaIDePKoIOALASGiLyQlHEHAAQEhogN48qgg4AsBIaIvJCUcQcABASGiA3jyqCDgCwEhoi8kJRxBwAEBIaIDePKoIOALASGiLyQlHEHAAQEhogN48qgg4AsBIaIvJCUcQcABASGiA3jyqCDgCwEhoi8kJRxBwAEBIaIDePKoIOALASGiLyQlnOAQwMNbLCJEjCWnAtYzFI/fJkTMk2Sysil4JGeFY3zr8B8Tm5krGYIIEUPIhch1CMHjtwnh+/fvE4dVaSIy2ZiZ+szQx5fOmzdvzMdKPRYilgp//JGH4vHbRBLC4aKjFhHN+0I6FiKGlBsR6hKKx28NHd7bcFJVj4i498DhVWguM4SIOgdlnwmBkDx+872Hh3GkHhFxaMV9eHpL+2DNBICnh4SInoCcyMGE4vGbxhgsHlKLiOlvQhpujh49GkTWCRGDyIawlIjR4zd+S1l+TUstIuJ60RRc7+MUOQQRIoaQCy2mQxkev6mSdnV1Vbavv/5azZs3LznHrePNmzcTn6dUpbXge9Vcvk1fL2MvRCwD9RaLMxSP3yastJiaraYsgEOXhSl4IdfflOb1Mo6FiGWg3mJxhuDx24SU7z6sISsDm9+ALJbDMm30M7LU+I4dO8zHSj0WIpYKf2tEHpPHb74T8fid/l4sOyeEiGXnQMDxM0ys7PGaE8XjtxAxYCKUrZrv9SfKTk/I8QsRQ86dknUTIhaXAULE4rCOLiYhYnFZJkQsDuvoYhIiFpdlQsTisA46Jl/r2LskstkRPS5xhfasEDG0HAlIH7GIxWWGELE4rKOLSYhYXJYJEYvDOrqYhIjFZZkQsTiso4tJiFhclgkRi8M6upgmyqiWEDJGiBhCLogOEx4BIeKELwICQAgICBFDyAXRYcIjIESc8EVAAAgBASFiCLkgOjgjgGe2ly9fZtqeP3+euGAcGhpSjbaRkRFnPesFIESsh4zH62Rgowy+d++eunr1aqbt0qVLibsHXD5k2Y4cOaIOHTqUedu1a5fq6elpasPl/aZNm6w2vHLjbS2ULS8yChE9Eq5WUMwEX7lyZTAFKZQCHaseQsRapTyCa2RcyIUOT2a21qnWfdu3b2/KGmI99+/fb22BT5w4YWXpz5w5k6lGQU3k+vXr6q+//mpYa6FGMzw8nFuJE4uYG7T/Dxir2KhqSgZn/b5JO839f6xyFBMCQsSYckt0bVkEhIgtm7WSsJgQECLGlFuia8siIERs2ayd2Al7/Pix6u7uHuPJO8TVjckpIeLELq8tmXqWXMOJMK3VuN8wJc/Vjc14mj0WIjaLmNwfDQIsF2cSMe/VjV2AESK6oCfPBo1Amog2qxuXlSAhYlnIS7y5I5Am4nirG+euUIMIhIgNwJG/4kYgTURSw7Xz588nCXv37l2yUOncuXNLT6gQsfQsEAXGQyCrv9NaRMR/a19fn2KJNgjJAHTuK1uEiGXngMSfGwK1iJiOrNbqxul7ijgXIhaBssRRCgK1iFhvdeNSFDQiFSIaYMhhayBAP2Jvb6+aM2eOWrJkiRoYGFCjo6NJ4uqtblx2yoWIZeeAxF8oAo1WNy5UkVRkQsQUIHIqCJSBgBCxDNQlTkEghYAQMQWInAoCZSAgRCwDdYlTEEghIERMASKngkAZCAgRy0Bd4hQEUgj8D8ysUgJDIFWjAAAAAElFTkSuQmCC[/img][br]Quotient [math] Q(x) = x^2 - 5x - 9 [/math] and Remainder [math] R = - 19 [/math] [br][br](c) [math] 2x^4+5x^2-3x-7 \div ( 2x-1 ) [/math] [br]Solution:[br][img]data:image/png;base64,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[/img][br][math] \therefore [/math] Quotient [math] Q(x) = x^3 +\frac{1}{2} x^2 + \frac{11}{4} - \frac{1}{8} [/math] and Remainder [math] ( R ) = \frac{-57}{8} [/math] [br][br](d) [math] y^5 +y^3 - y \div (3-y) [/math] [br]Solution:[br][img]data:image/png;base64,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[/img][br][math] \therefore [/math] Quotient [math] Q(y) = -y^4 - 3y^3 - 10y^2 - 30y - 89 [/math] and Remainder [math] ( R ) = 267 [/math][br][br]4. For the function [math] f(y) = y^3 – y^2 – 17y – 15,[/math] use long division to determine whether each of the following is a factor of [math] f(y) [/math] or not.[br][br](a) [math] y + 1 [/math] [br]Solution:[br][img]data:image/png;base64,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[/img][br]Here, remainder is 0. So [math] y+1 [/math] is a factor of [math] f(y) [/math] [br][br](b) [math] y + 3 [/math] [br]Solution:[br][img]data:image/png;base64,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[/img][br]Since, remainder is 0, [math] y+3 [/math] is a factor of [math] f(y) [/math] [br](c) [math] y + 5 [/math] [br]Solution:[br][img]data:image/png;base64,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[/img][br]As remainder [math] = - 80 \neq 0 [/math], [math] y+5 [/math] is not factor of [math] f(y) [/math] [br](d) [math] y - 1 [/math] [br]Solution:[br][img]data:image/png;base64,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[/img][br]As remainder [math] = -32 \neq 0 [/math], [math] y - 1 [/math] is not a factor of [math] f(y) [/math].[br][br](e) [math] y - 5 [/math] [br]Solution:[br][img]data:image/png;base64,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[/img][br]As remainder [math] = 0 [/math], [math] y -5 [/math] is a factor of [math] f(y) [/math] [br][br]5. For the polynomial [math] p(x) = x^4 – 6x^3 + x – 2 [/math] and divisor [math] d(x) = x – 1, [/math] use long division to find the quotient [math] Q(x) [/math] and the remainder [math] R(x) [/math] when [math] P(x) [/math] is divided by [math] d(x).[/math] Express [math] p(x) [/math] in the form of [math] d(x). Q(x) + R(x). [/math] Write your finding.[br]Solution:[br]Here,[br] [math] p(x) = x^4 - 6x^3 + x - 2 [/math][br] [math] d(x) = x-1 [/math][br]Now,[br] 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RNJ1ieZPz780dqUnBMVwAPEcspdbfuLFy+M/RPNz89H/pfEv+vExISxf3FECAMDA6lFKYiQurq6jEVhiPBaWloyF72qCLNt0YqTomKTKtOW7BD45ZdfjLS1+W14b968ifxnWO7P0rYoBWcDRSU710SsmmDisidPnsjGxkasfHgwCVBUeA7I+/fv5c6dOx4JzFONKVeZSCAqAYpKVHIZOg6N3zdu3PBqNDs7K5halokEohKgqEQll8HjMC81Bud2dfbHDLrEySpRVJx028dGP3r0yHvygb4o7e3tcvXqVUHDo2rCvnNzc3L37l3nRWVnZ0fu3bsnDx8+9JiMj4+rYuB+GghQVDRAtCELDFPZ3Nws6EDX398vYXr3IkLBdCJIL1++lM8++0ypSjbOC416QFD8hAbo+vp6mZqa8jfx0zABiophwEllD1GJmhCdILpBevv2rdTV1SllZeN4uxC6EydOyOrqaqEOEFssTMkQoKgkw9l4KbjAEXEsLi7K2traR+WhARa3AVtbW95j45mZGVleXvb2Q3SCf/KjoyPBvNWqAhVWVCrZ8JHBETegDrdv35Z3794VckDDM24HmZIhQFFJhrPxUnCBYzZGtI3gHRNMZu8n9NbFbQDSmTNnPAGZnJyUhoYGfxdPkHBcmNumMKKiYkPBGI0rqDcir2DkojF7ZlWCAEWlBBQXNxWLAbp3j42NeWKBWwIktDfU1tZ629A3ZW9vL1ZVVUUFEZQpG6pVAA3XIyMj1Xbj7xoJUFQ0wtSZVdg5oNHXJJhaW1s/6m+CC7upqSm4m/K6rnmhVW0IW/9SFRkeHla+lSt1PLdFI0BRicbNqqOePXsmNTU1x7rY4+W64sZJPBXye86iAvv7+7HqoRqpBAvRbUMw7+A6XjnA4ife/vgkzH9SVMwzNl4CbmVwsQZTY2Oj98b0ysqKDA4Oej9hG/qiIG1vb8v6+nrwkNDrqqJi0oZSRqNt6PHjx15jLRps8R2vHzAlQ4Cikgxn46XgIsITncPDQ68D261bt7wy8R4PohbcTqBtAU93FhYWtPTbUBUVkzYUg8Vt4MmTJ73IDdGbv6BhmikZAhSVZDgnUgouKEQixe0reALid27D0yFENjqSqqigLFM26KgH89BLgKKil2eucuO80Llyt3JlKSrKqLK9IyIJm8dTQXSFznN4r4fJbgIUFbv9k4h1uGD9p0I2jqeCp1RoM0J/l5s3bwoeFTPZS4CiYq9vErMMbTA2j6eCRubu7m6PByKq06dPJ8aGBYUnQFEJzyyzRyASsHE8FfQW9sdixe3PuXPnMuuDLFSMopIFL4qI7eOpxLXPd1NHR0fs/jV+Xvw0Q4CiYoZr4rni8a7N46nEsc+HiZcSS72B7f/OTzsIUFTs8ENsK3DRRk1JjKcSxz7UC71iMUSDvx61rjzOPAGKinnGiZSAi9bm8VTi2Ifo5NSpU94IbhjFrfidpkQAsxBlAhQVZVR274iLFk9JbB1PJa59dtOndUECFJUgDYfXbR5PBVjTsM9hdzptOkXFUveFHU+k+H0f28ZTMW2fpW7MpVkUlQy43fbxVNKyLwOudbIKFBUn3XbcaNvHU0nLvuOU+C0pAhSVpEgbLsfm8VRQ9TTsM4yc2ZchQFEpA8bFzWi3sHU8FfBM2j4XfZgFmykqWfBiSnXgeCopgbe8WIqK5Q6ieSTgGgGKimseK7IXU15gVj4mErCFAEXFFk9EtAM9VTHGCBMJ2EKAomKLJyLaQVGJCI6HGSNAUTGGNpmMKSrJcGYp6gQoKuqsrNyTomKlW3JtFEXFIffrms84TpXDvpMUpywe6yYBioqbfitYzUilgIIrlhCgqFjiiKhmUFSikuNxpghQVEyRTShfikpCoFmMMgGKijIqO3ekqNjplzxbRVFx3Pt8/8ZxB2bQfIpKBp3KKpFAmgQoKmnSZ9kkkEECFJUMOpVVIoE0CVBU0qTPsnNFANOnHBwchFrevHkjm5ubZRd/jmmbQFJUbPKGRbZgSg3VC2B3d7fsSR+8IF68eCFLS0tKy/T0tGCaU5VldHRUhoaGqi4DAwPS09OjtHR2dkpbW5vScvnyZblw4UJqi23CQlH574UMxwQvAH/9X//6l9aLQPUC6OvrUzr5cZGoXgAtLS2pnfhpXnRZL5uiYtG/sW8Kxk69ePEiL7gU/23jXPgQS5WoAuKrGqkgqlGJfrDPxMSEUkSF6Es1UvP3wxzS/h9cqU9EibYlRioiAqWPc1KHOVb1Aujq6tJ+ASBKUrmdwD7z8/PKFwBua0qd8MXbcAGo3lKh/YHJTQIUlf/6DdFK8UWA7/v7+0oXAi8CNy8AWq2fAEVFP1PmSAK5JkBRybX77ao8ZjKcnZ2VnZ0duwyjNaEIUFRC4eLOpgjgNhOzGH748EFu3rwpw8PDpopivoYJUFQMA2b2agQwolx3d7e3M2YHOH36tNqB3Ms6AhQV61yST4PQ2c7vb4Hbn3PnzuUTRAZqTVHJgBNtqcKjR4+8R/PoD9Le3i5Xr16VKE/FOjo6ZH193ZZqRbIDwnjv3j15+PChx2R8fDxSPi4eRFFx0WuW2owBo5qbmwXd1vv7+wXRR9iEPjJra2vKh9k4QyMGKIeg+Am3c/X19TI1NeVvyvQnRSXT7k22chCVOAm9R1++fOllgXWVZOPIdxC6EydOyOrqaqEKEFsseUgUlTx4OaE64gLH05vFxcWS0QYeF+M2YGtrSzY2NmRmZkaWl5c96xCdnDp1yvtHx7+66gUYVlQq2aALE+a2vn37trx7966Q5ZUrV7zbwcKGDK9QVDLs3KSrhgscT3HQjoJI49KlSwUTcFvjz/l85swZ71ZgcnJSGhoaCvtEWQkjKqZsqGY36l1XV3cscql2jMu/U1Rc9p5lthe3oeCdqLGxMS96wS0BEtobamtrvW3o7La3txerFqqiggjKlA3VKoCG65GRkWq7ZeZ3ikpmXKm/ImFnI8T7U8HU2toqCPuDCRd2U1NTcJPyuq4ZGlVtCFv/UhVBJz4IX54SRSVP3jZY12fPnklNTY3XVuIXgzeyi9tG8FTozp07/i7eC5uFLxFWVCOVYNa6bQjmHVx/8uSJYPFTsOHW35bFT4pKFr2aQp1wK4OLNZgaGxu9oRZWVlZkcHDQ+wnb5ubmvPXt7e3Y/VFURcWkDcE6++toU8JrB2isxYLv9+/f93/O9CdFJdPuTbZyuIjwROfw8FDu3r0rt27d8gx48OCBIGrB7QTaFnp7e2VhYUFLvw1VUTFpQzFl3AaePHnSi9wQvfkLGqbzkCgqefBygnXEBYVIpLh9BU9A0CaChKdDiGx0JFVRQVmmbNBRjyzlQVHJkjdzWBfO0Gif0ykq9vmEFpGA0wQoKk67j8aTgH0EKCr2+YQWkYDTBCgqTruPxpOAfQQoKvb5hBaRgNMEKCpOuy9bxnPg62z4k6KSDT86XwsOfO28CwsVoKgUUHAlTQLobcuBr9P0gL6yKSr6WDKnGAQ48HUMeJYdSlGxzCEum2P7wNe67HPZR0nYTlFJgnJOysB7OBjqwNaBr3XYlxNXxqomRSUWPh4cJICLNk7C8AAmB76Oa1+cuuXpWIpKnrxtuK64aG0e+DqOfYbRZSp7ikqm3JluZXDR4imOrQNfp2Ffuh5Jp3SKSjrcM1mqzQNfA3ga9mXS0VUqRVGpAijPP4cd+Ll4YCbbBr42bV+ez5Vg3SkqQRpcj0zA9oGv07IvMlCHD6SoOOw8m0y3feDrtOyzyUdJ2UJRSYp0DsqxeeBr4E/Dvhy4/aMqUlQ+QsINcQjYPPA16pW0fXFYunosRcVVz9FujwAHvrbvRKCo2OcTWkQCThOgqDjtPhpPAvYRoKjY5xPrLcIE50dHR9bbSQPTIUBRSYe706Wiuztm+2MigVIEKCqlqHBbRQIUlYp4cv8jRSX3p0B4ABSV8MzydARFJU/e1lRXioomkBnNhqKSUcfqqtavv/4q169fl2vXrhWW8+fPS0dHR+E7foPQJJnCvuyYpG15L4uikvczIEL9GalEgJajQygqOXK2rqpSVHSRzGY+FJVs+tVorSgqRvE6nzlFxXkXJl8BikryzF0qkaLikrcssZUv8VniCEvNoKhY6hiaRQKuEqCouOo52k0ClhKgqFjqGJpFAq4SoKik7DmMRLa5ufnRcnBwINWW4iknUq4KiycBjwBFJcUT4dWrV3Lx4kW5cOGC8aWlpUXa2trKLp2dndLT01N26evrk6GhobLL6Oio/PDDD2WX6elpWVpaqrq8ePHiI4EtJbq7u7tVRdcXZYpvsic5RSVZ3sdKQ5SSlKgkIVwul4FJ5dMUXQjy/Px8JNGFwNqUKCopewPRSql/YpV/dZyElaKD4G+IJCpFGgMDA2WjFEQwXV1dFS86REIui4rrtuM8siVRVGzxRMbtwPzK/u1IpU/865YS2eJtuE1SEV7soyK+ExMTTouuTdEKRSXjFzOr5w4BtP1UElz8Vkp0bYpSQJui4s45R0tJwAkCFBUn3EQjTRPgQN76CFNU9LFkTo4SwOwA7e3tqVi/s7Mj9+7dk4cPH3oN3ePj46nYobNQiopOmszLOQKHh4fS1NSUiqhgVD0Iip8wQ0F9fb1MTU35m5z8pKg46TYarYsAhnEYGRlJRVQQIZ04cUJWV1cL1WlubhYsLieKisveo+2xCOBi3t7eLikqs7OzgluRra0t2djYkJmZGVleXo5VXvHBaMe5ffu2vHv3rvDTlStX5OrVq4XvLq5QVFz0Gm2OTQD9ZtA5EKk4UsF2f7K0M2fOeLcjk5OT0tDQELvcShmgzLq6umORS6X9bf2NomKrZ2iXUQKPHj2SDx8+eGUERQXbcFuChDaP2tpab7/379/L3t6eUZvw/hVscT1RVFz3IO33CISZsmN9fV2eP39eIBcUlcJGEU9c0IhbLYUpu1xew8PDiU9zUs6WuNspKnEJ8njnCOD25ubNm4Xliy++kM8//9z7jujET/39/XLnzh3/q+zv7xfWda48efJEsPgp2HDrb3Ppk6LikrdoqxEC6KPi91NZWVmRwcFBr5zGxkaZm5vz1tGgiwhHd3r69Kk8fvzYa6xFgy2+379/X3cxieZHUUkUNwuzjcDY2JgXpZw9e1aw/uDBA8Eb17ilwW1Rb2+vLCwsGOk7gqEvTp48KTU1NccWNAq7nCgqLnuPthshgKcw/m0QnhKhkZZJnQBFRZ0V9yQBElAgQFFRgMRdSIAE1AlQVNRZcU8SIAEFAhQVBUjchQRIQJ0ARUWdFfckARJQIEBRUYDEXUiABNQJUFTUWXHPjBOwZfQ3W+yI6m6KSlRyPC5TBNIc/S0I0hY7gjaFXaeohCXG/TNHwMTobxCHsBGHCTvScBZFJQ3qLNMqAiZGf0Oe/pgsqpU1YYdq2Tr3o6jopMm8nCNgavS3sKJSyQ7XoFJUXPMY7dVGwOTob2FEpZId2iqbYEYUlQRhsyi7CJgc/S2MqJSzwy5a6tZQVNRZcU/LCYQZgU3n6G94o/n69ety7dq1wnL+/Hnp6OgofMdvEJripGpH8XE2f6eo2Owd2maMgOnR31QjFVU7jIEwkDFFxQBUZukeAd2jv6mKSjGpoB3Fv7nynaLiiqdopzECJkZ/iyIqxXYYq7DhjCkqhgEzezcJxB39LYqouEnqY6spKh8z4RYSiE3gp59+ip2HqxlQVFz1HO2uSCBKN/mKGfJHZQIUFWVU3NElAnm+/UjbTxSVtD3A8o0QoKgYwaqUKUVFCRN3co0ARSU9j1FU0mPPkg0SoKgYhFsla4pKFUD82X4CcbrJ66pdmFcEdJVpaz4UFVs9Q7tiEWCkEgtfrIMpKrHw8WBbCVBU0vMMRSU99izZIAGKikG4VbKmqFQBxJ/dJEBRSc9vFJX02LNkgwTy3E3eIFalrCkqSpi4EwmQgCoBiooqKe5HAiSgRICiooSJO5EACagSoKiokuJ+FQm8fv1aNjc3yy5v3ryRg4ODSAtGm2dyhwBFxUwJprEAAAMBSURBVB1fWWvpq1ev5OLFi3LhwgVrlpaWFmlra6u6dHZ2Sk9Pj9LS19cnQ0NDSsvExIRg/Nlqy/T0tCwtLSktT58+LSvaEPTd3V0rzhGKihVucNsIRCm2iYpNApekLRD4tBNFJW0PZKR8nMylbn9U/oXn5+er/qP7//ijo6NKkYIfUQwMDChFIeWila6urqrRTqmI6PLly6lEbTZEKxSVjFzUrIabBNBepNrWhHapUsLtb7MhSoEXKCpunou0mgSsJUBRsdY1NIwE3CRAUXHTb7SaBKwlQFGx1jU0jATcJEBRcdNvtJoErCVAUbHWNTSMBNwkQFFx02+0mgSsJUBRsdY1NCwvBFZXV6W3t1cmJyflwYMH8vbtW6erTlFx2n003nUCz58/l2+//bZQjbNnz8r3339f+O7iCkXFRa/R5swQ+PLLL2VxcbFQH4iM66PWUVQK7uQKCSRLYGdnR2pqauTo6EhmZmZkdnZWPnz4kKwRBkqjqBiAyixJQIUAhOSTTz6RqakpT0x+/PFH+eabb+T9+/cqh1u7D0XFWtfQsKwTQMMsIpWXL18Wqtra2ird3d2F7y6uUFRc9BpttpZAmOlPcbsDUQkmCMpXX30V3OTc+vEaOWc+DSYBdwngdgeiEmxHuXHjhnz99dfuVopDHzjtOxqfAQKIStbX1ws1+e6777w+K4UNDq4wUnHQaTQ5OwQ2NjakublZ9vb2ZGFhQTBiHJ4GuZwoKi57j7ZngsDPP/8sc3Nzsra2lon6UFQy4UZWggTsIUBRsccXtIQEMkGAopIJN7ISJGAPAYqKPb6gJSSQCQIUlUy4kZUgAXsIUFTs8QUtIYFMEKCoZMKNrAQJ2EOAomKPL2gJCWSCAEUlE25kJUjAHgIUFXt8QUtIIBMEKCqZcCMrQQL2EKCo2OMLWkICmSBAUcmEG1kJErCHAEXFHl/QEhLIBAGKSibcyEqQgD0EKCr2+IKWkEAmCFBUMuFGVoIE7CFAUbHHF7SEBDJBgKKSCTeyEiRgD4H/AyXVxGpQ68YBAAAAAElFTkSuQmCC[/img][br]Hence, Quotient [math] Q(x) = x^3 - 5x^2 - 5x -4 [/math][br]  Remainder [math] (R) = -6 [/math][br]We know,[br]  [math] p(x) = d(x). Q(x) + R(x) [/math][br][math] \therefore x^4 - 6x^3 + x -2 = (x-1)(x^3-5x^2-5x-4) - 6 [/math]
– AMBIK BARAL

2.2.

–

2.3.

–

2.4.

–

3.

Trigonometry

  • 1. Multiple Angles
  • 2. Sub-Multiple Angles
  • 3. Transformation Of Trigonometric Formula
  • 4. Conditional Trigonometric Identities
  • 5. Trigonometric Equations

3.1.

Multiple Angles

Multiple Angles
Exercise - 5.1 [ Page - 157 ][br]1. (a) Define multiple angle with an example.[br]Solution:[br]If A be any angle then 2A, 3A,.... etc are called multiple angles of A.[br][br]1. (b) Write [math]\cos2A[/math] in terms of [math] \cos A [/math] and [math]\sin A[/math][br]Solution: [br][math]\cos2A = 2\cos^2 A-1 [/math][br][math] \cos2A = 1- 2\sin^2 A [/math][br][br]2. (a) Write [math] \sin 2A [/math] in terms of [math] \tan A [/math][br]Solution:[br][math]\sin 2A = \frac{2 \tan A}{ 1-\tan^2 A } [/math][br][br]2(b) Write [math] \tan^2 A [/math] in terms of [math] \cos2A [/math][br]Solution:[br][math] \tan^2 A = \frac{1-\cos 2 A }{1+ \cos 2 A } [/math][br][br]2(c) Write [math] \sin3A [/math] in terms of [math] \sin A [/math].[br]Solution:[br][math] \sin 3A = 3\sin A - 4\sin^3 A [/math][br][br]2(d) Write [math]\tan3θ [/math] in terms of [math] \tan \theta[/math][br]Solution:[br][math] \tan 3\theta = \frac{ 3 \tan \theta -\tan^3 \theta}{1-3\tan^2 \theta} [/math][br][br]3.(a) If [math] \sin A = \frac{3}{5}[/math], find the value of [math] \cos 2A [/math].[br]Solution:[br]Given,[br][math] \sin A =\frac{3}{5} [/math][br]Now,[br][math] \begin{align} \cos 2A &=1-2\sin^2 A\\ \ &=1-2\times\left(\frac{3}{5} \right)^2\\ \ &= 1-\frac{18}{25}\\ \ &=\frac{25-18}{25}\\ \ &=\frac{7}{25}\\ \therefore \cos 2A &= \frac{7}{25} \end{align}[/math][br][br]3. (b) If [math] \sin 2A = \frac{ 24}{25} [/math] and [math] \sin A = \frac{4}{5}[/math] , then find the value of [math] \cos A [/math].[br]Solution:[br]Given,[br][math] \sin 2A = \frac{ 24}{25} [/math] and [br][math] \sin A = \frac{4}{5} [/math][br]We know that,[br][math] \begin{align} \sin 2A &=2\sin A \cos A \\ or,\frac{24}{25}&=2\times \frac{4}{5}\times \cos A\\ or,\frac{24}{25}&=\frac{8}{5}\times \cos A\\\\ or, \frac{3}{5}&=\cos A\\ \therefore \cos A &=\frac{3}{5} \\ \end{align} [/math][br][br]3(c) If [math] \sin A = \frac{4}{5} [/math], find the value of [math] \sin 2A [/math].[br]Solution:[br]Given[br][math] \sin A = \frac{4}{5} [/math][br]Now,[br][math] \begin{align} \sin 2A &=2\sin A \cos A\\ \ &=2\times \frac{4}{5}\times \frac{3}{5}\\ \ &= \frac{24}{25}\\ \therefore \sin 2A &= \frac{24}{25} \end{align} [/math][br][br]3(d) [math] \cos \theta = \frac{12}{13} [/math], find the value of [math] \sin 2\theta [/math] and [math] \cos 2\theta [/math].[br]Solution:[br]Given,[br][math] \cos \theta = \frac{12}{13} [/math][br]Now,[br][math] \begin{align} \cos 2\theta &=2\cos^2 \theta -1 \\ \ &=2\times\left(\frac{12}{13} \right)^2-1\\ \ &=2\times\left(\frac{144}{169} \right)-1\\ \ &= \frac{288}{169}-1\\ \ &=\frac{288-169}{169}\\ \ &=\frac{119}{169}\\ \therefore \cos 2\theta &= \frac{119}{169} \end{align} [/math][br]Again,[br][math] \begin{align} \sin 2\theta &= \sqrt{1- \cos^2 2\theta}\\ \ &=\sqrt{1-\left(\frac{119}{169}\right)^2}\\ \ &=\sqrt{1-\frac{14161}{28561}}\\ \ &=\sqrt{\frac{28561-14161}{28561}}\\ \ &=\sqrt{\frac{14400}{28561}}\\ \ &=\frac{120}{169}\\ \therefore \sin 2\theta &=\frac{120}{169} \end{align} [/math][br][br]3(e) If [math] \tan \theta = \frac{3}{4} [/math], find the value of [math] \sin 2\theta [/math] and [math] \tan 2\theta [/math][br]Solution:[br][math] \begin{align} \sin 2\theta &= \frac{2\tan \theta}{1+\tan^2 \theta }\\ \ &= \frac{2\left( \frac{3}{4} \right)}{1+ \left( \frac{3}{4} \right)^2} \\ \ &=\frac{\frac{6}{4}}{1+\frac{9}{16}}\\ \ & = \frac{\frac{6}{4}}{\frac{16+9}{16}}\\ \ & = \frac{\frac{6}{4}}{\frac{25}{16}}\\ \ & = \frac{6}{4}\times \frac{16}{25}\\ \ & = \frac{24}{25}\\ \therefore \sin 2\theta &= \frac{24}{25}\\ \end{align} [/math][br]And[br][math] \begin{align} \tan 2\theta &= \frac{2\tan \theta}{1-\tan^2 \theta }\\ \ &= \frac{2\left( \frac{3}{4} \right)}{1- \left( \frac{3}{4} \right)^2} \\ \ &=\frac{\frac{3}{2}}{1-\frac{9}{16}}\\ \ & = \frac{\frac{3}{2}}{\frac{16-9}{16}}\\ \ & = \frac{\frac{3}{2}}{\frac{7}{16}}\\ \ & = \frac{3}{2}\times \frac{16}{7}\\ \ & = \frac{24}{7}\\ \therefore \tan 2\theta & = \frac{24}{7}\\ \end{align} [/math][br][br]3. (f) If [math] \sin \alpha = \frac{1}{2} [/math], find the value of [math] \sin 3\alpha [/math] and [math] \cos 3\alpha [/math][br]Solution:[br][math] \begin{align}\sin 3\alpha &=3\sin \alpha -4\sin^3 \alpha \\ \ & = 3\left(\frac{1}{2}\right)-4\left(\frac{1}{2}\right)^3\\ \ & = \frac{3}{2}-4\times \frac{1}{8} \\ \ & = \frac{3}{2} - \frac{1}{2}\\ \ & = \frac{3-1}{2} \\ \ & = \frac{2}{2} \\ \ & = 1 \\ \therefore \sin 3\alpha &= 1 \\ \end{align} [/math][br]And[br][math] \begin{align} \cos 3\alpha &= \sqrt{1- \sin^2 3\alpha}\\ \ &=\sqrt{1-1}\\ \ & = \sqrt{0}\\ \ & = 0\\ \therefore cos 3\alpha &= 0 \\ \end{align} [/math][br]Alternative[br] [math] \begin{align} \sin \alpha &= \frac{1}{2} \\ or, \sin \alpha & = \sin 30^{\circ} \\ \therefore \alpha & = 30^{\circ}\ \end{align} [/math][br]Now[br][math] \begin{align} \sin 3\alpha &= \sin 3(30^{\circ})\\ \ &= \sin 90^{\circ} \\ \ & = 1\\ \therefore \sin 3\alpha &=1 \end{align} [/math][br][br]And[br][math] \begin{align} \cos 3\alpha &= \cos 3(30^{\circ})\\ \ &= \cos 90^{\circ}\\ \ & = 0\\ \therefore \cos 3\alpha &=0 \end{align} [/math][br][br]3. (g) If [math] \cos \alpha = \frac{ \sqrt{3}}{2} [/math], find the value of [math] \sin 3\alpha [/math] and [math] \cos 3\alpha [/math][br]Solution:[br][math] \begin{align} \cos \alpha &= \frac{\sqrt{3}}{2} \\ or, \cos \alpha & = \cos 30^{\circ} \\ \therefore \alpha & = 30^{\circ}\\ \end{align} [/math][br]Now,[br][math] \begin{align} \sin 3\alpha &= \sin 3(30^{\circ})\\ \ &= \sin 90^{\circ} \\ \ & = 1\\ \therefore \sin 3\alpha &=1 \end{align} [/math][br][br]And[br][math] \begin{align} \cos 3\alpha &= \cos 3(30^{\circ})\\ \ &= \cos 90^{\circ} \\ \ & = 0\\ \therefore \cos 3\alpha &=0 \end{align} [/math] [br][br]3. (h) If [math] \tan \beta = \frac{1}{2} [/math], find the value of [math] \tan 3\beta [/math].[br]Solution:[br]Given,[br][math] \tan \beta = \frac{1}{2} [/math] [br]Now,[br][math] \begin{align} \tan 3\beta &=\frac{3 \tan \beta -\tan^3 \beta}{1-3\tan^2 \beta}\\ \ &= \frac{3 \left(\frac{1}{2} \right)-\left(\frac{1}{2} \right)^3}{1-3\left(\frac{1}{2} \right)^2}\\ \ & = \frac{\frac{3}{2}-\frac{1}{8}}{1-\frac{3}{4}} \\ \ & = \frac{\frac{12-1}{8}}{\frac{4-3}{4}} \\ \ & = \frac{11}{8} \times \frac{4}{1} \\ \ & = \frac{11}{2}\\ \therefore \tan 3\beta &= \frac{11}{2}\\ \end{align} [/math][br][br]4. (a) If [math] \cos 2A = \frac{7}{25} [/math], then show that [math] \sin A = \frac{3}{5} [/math] [br]Given,[br][math] \cos 2A = \frac{7}{25} [/math][br]We know that,[br][math] \begin{align} \sin^2 A &=\frac{1-\cos 2A}{2}\\ \ & = \frac{1-\frac{7}{25}}{2}\\ \ & = \frac{\frac{25-7}{25}}{2}\\ \ & = \frac{\frac{18}{25}}{2}\\ \ & = \frac{18}{25}\times \frac{1}{2}\\ \ & = \frac{9}{25} \\ or, \sin^2 A & = \frac{9}{25}\\ or, \sin A & = \sqrt{\frac{9}{25}}\\ \therefore \sin A & = \frac{3}{5} \end{align} [/math][br][br]4.(b) If [math] \cos 2A = - \frac{ 1}{2} [/math], then show that [math] \cos A = \frac{1}{2} [/math].[br]Solution:[br]Given,[br][math] \cos 2A = - \frac{ 1}{2} [/math][br]We know that,[br][math] \begin{align} \cos^2 A &=\frac{1+\cos 2A}{2}\\ \ & = \frac{1+\left( \frac{-1}{2}\right) }{2}\\ \ & = \frac{\frac{2-1}{2}}{2}\\ \ & = \frac{\frac{1}{2}}{2}\\ \ & = \frac{1}{4}\\ or, \cos^2 A & = \frac{1}{4}\\ or, \cos A & = \sqrt{\frac{1}{4}}\\ \therefore \cos A & = \frac{1}{2}\\ \end{align} [/math][br][br]5. (a) Prove that: [math] \sin A = \pm \sqrt{\frac{1-\cos 2A}{2}} [/math][br]Solution:[br]First Method:[br][math] \begin{align} \cos 2A &= 1-2\sin^2 A\\ or, 2 \sin^2 A&=1-\cos 2A\\ or, \sin^2 A & = \frac{1-\cos 2A}{2}\\ \therefore \ \sin A&= \pm\sqrt{\frac{1 \cos 2A}{2}}\\ \end{align} [/math][br]Second Method:[br][math] \begin{align} \text{ RHS } & = \pm\sqrt{\frac{1-\cos 2A}{2}}\\ \ & = \pm\sqrt{\frac{1-(1-2\sin^2 A)}{2}}\\ \ & = \pm\sqrt{\frac{1-1+2\sin^2 A}{2}}\\ \ & = \pm\sqrt{\frac{2\sin^2 A}{2}}\\ \ & = \pm\sqrt{\sin^2 A}\\ \ & = \pm \sin A\\ \ & = \sin A\\ \ & = \text{ LHS } \\ \end{align} [/math][br][br]5. (b) Prove that: [math] \cos A = \pm \sqrt{\frac{1+\cos 2A}{2}} [/math][br]Solution:[br]First Method:[br][math] \begin{align} \cos 2A &= 2\cos^2 A -1\\ \cos 2A +1&= 2\cos^2 A \\ or, 2 \cos^2 A&=1+\cos 2A\\ or, \cos^2 A & = \frac{1+\cos 2A}{2}\\ \therefore \ \cos A&= \pm\sqrt{\frac{1+\cos 2A}{2}}\\ \end{align}[/math][br]Second Method:[br][math] \begin{align} \text{ RHS } & = \pm\sqrt{\frac{1+\cos 2A}{2}}\\ \ & = \pm\sqrt{\frac{1+(2\cos^2 A-1)}{2}}\\ \ & = \pm\sqrt{\frac{1+2\cos^2 A-1}{2}}\\ \ & = \pm\sqrt{\frac{2\cos^2 A}{2}}\\ \ & = \pm\sqrt{\cos^2 A}\\ \ & = \pm \cos A\\ \ & = \cos A\\ \ & = \text{ LHS } \\ \end{align} [/math][br][br]5. (c) Prove that: [math] \tan A = \pm \sqrt{\frac{1-\cos 2A}{1+\cos 2A }} [/math][br]Solution:[br][math] \begin{align} \text{ RHS } & = \pm\sqrt{\frac{1-\cos 2A}{1+\cos 2A}}\\ \ & = \pm\sqrt{\frac{1-(1-2\sin^2 A)}{1+(2cos^2A+1)}}\\ \ & = \pm\sqrt{\frac{1-1+2\sin^2 A}{1+2\cos^2A-1}}\\ \ & = \pm\sqrt{\frac{2\sin^2 A}{2\cos^2 A}}\\ \ & = \pm\sqrt{\tan^2 A}\\ \ & = \pm \tan A\\ \ & = \tan A\\ \ & = \text{ LHS } \\ \end{align} [/math][br][br]5. (d) Prove that: [math] \sec 2A = \frac{\cot^2 A + 1}{ \cot^2 A -1 } [/math][br]Solution:[br][math] \begin{align} \text{LHS} & = \sec 2A \\ \ & =\frac{1}{\cos 2A} \\ \ & = \frac{\cos^2 A+ \sin^2 A }{\cos^2 A -\sin^2 A}\\ [\because &\text{ Dividing both sides by } \sin^2 A]\\ \ & =\frac{\frac{\cos^2 A }{\cos^2 A}+\frac{\sin^2 A}{\cos^2 A}}{\frac{\cos^2 A }{\cos^2 A}-\frac{\sin^2 A}{\cos^2 A}}\\ \ & = \frac{\cot^2 A-1}{\cot^2 A +1}\\ \ & = \text{RHS} \end{align}[/math][br][br]6. (a) [math] \frac{\sin 2A}{1+\cos 2A } = \tan A [/math][br]Solution:[br][math] \begin{align} \text{ LHS } & = \frac{\sin 2A}{1+\cos 2A }\\ \ & = \frac{2\sin A \cos A }{1+ 2\cos^2 A -1 }\\ \ & = \frac{2 \sin A \cos A }{2\cos^2 A } \\ \ & = \frac{ \sin A }{ \cos A } \\ \ & = \tan A \\ \ & = \text { RHS } \end{align} [/math][br][br]6(b) [math] \frac{ 1 -\cos 2A }{ \sin 2A } = \tan A [/math][br]Solution:[br][math] \begin{align} \text { LHS } & = \frac{ 1 -\cos 2A }{ \sin 2A } \\ \ & = \frac{ 1 - (1 -2\sin^2 A ) } {\sin 2A } \\ \ & = \frac{ 1-1+2\sin^2 A}{2\sin A \cos A } \\ \ & = \frac{ 2\sin^2 A}{2\sin A \cos A} \\ \ & = \frac{ \sin A } { \cos A } \\ \ & = \tan A \\ \ & = \text { RHS } \\ \end{align} [/math][br][br]6. (c) [math] \frac{\sin 2A}{ 1-\cos 2A} = \cot A [/math][br]Solution:[br][math] \begin{align} \text{ LHS } & = \frac{\sin 2A}{ 1-\cos 2A}\\ \ & = \frac{2\sin A \cos A } {1-(1-2\sin^2 A)} \\ \ & = \frac{ 2\sin A \cos A}{1-1+2\sin^2 A}\\ \ & = \frac{ 2\sin A \cos A } {2\sin^2 A } \\ \ & =\frac{ \cos A}{\sin A } \\ \ & = \cot A \\ \ & = \text{ RHS } \\ \end{align} [/math][br][br]6. (d) [math] \frac{ 1-\cos 2\theta }{1+\cos 2\theta} = \tan^2 \theta [/math] [br]Solution:[br][math] \begin{align} \text{ LHS } & = \frac{ 1-\cos 2\theta }{1+\cos 2\theta} \\ \ & = \frac{ 1 - (1-2\sin^2 \theta ) }{ 1+ ( 2\cos^2 \theta - 1) } \\ \ & = \frac{ 1-1+2\sin^2 \theta }{1+2\cos^2 \theta-1} \\ \ & = \frac{ 2\sin^2 \theta} { 2\cos^2 \theta } \\ \ & = \frac{ \sin^2 \theta} { \cos^2 \theta} \\ \ & = \tan^2 \theta \\ \ & = \text{ RHS } \\ \end{align} [/math][br][br]6. (e) [math] \frac{1-\tan \alpha}{1+\tan \alpha}=\frac{1-\sin 2\alpha}{\cos 2\alpha} [/math][br]Solution:[br][math] \displaystyle \begin{align} \text{ LHS } & = \displaystyle \frac{1-\tan \alpha}{1+\tan \alpha}\\ \ & = \displaystyle \frac{ 1 - \frac{ \sin \alpha}{\cos \alpha}}{ 1+ \frac{\sin \alpha}{\cos \alpha}}\\ \ & = \frac{\frac{\cos \alpha - \sin \alpha}{\cos \alpha}}{\frac{\cos \alpha + \sin \alpha }{\cos \alpha}} \\ \ & = \frac{ \cos \alpha - \sin \alpha} { \cos \alpha + \sin \alpha } \\ \ & = \frac{ \cos \alpha - \sin \alpha} { \cos \alpha + \sin \alpha } \times \frac{ \cos \alpha - \sin \alpha} { \cos \alpha - \sin \alpha } \\ \ & = \frac{ (\cos \alpha - \sin \alpha)^2 } { \cos^2 \alpha - \sin^2 \alpha } \\ \ & = \frac{\cos^2 \alpha - 2\cos \alpha \sin \alpha + \sin^2 \alpha }{\cos 2\alpha } \\ \ & = \frac{\sin^2 \alpha + \cos^2 \alpha - 2\sin \alpha \cos \alpha }{\cos 2\alpha} \\ \ & = \frac{ 1 - \sin 2\alpha }{\cos 2\alpha }\\ \ & = \text{ RHS } \end{align} [/math][br][br]6. (f) [math] \frac{ \cos 2\theta}{1+\sin 2\theta } = \frac{ 1-\tan \theta}{1+ \tan \theta} [/math][br]Solution:[br][math] \begin{align} \text{LHS } & = \frac{ \cos 2\theta}{1+\sin 2\theta }\\ \ & = \frac{\cos^2 \theta - \sin^2 \theta }{\sin^2 \theta + \cos^2 \theta +2\sin \theta \cos \theta} \\ \ & = \frac{(\cos \theta - \sin \theta)(\cos \theta + \sin \theta)}{(\cos \theta + \sin \theta )^2} \\ \ & = \frac{\cos \theta - \sin \theta }{\cos \theta + \sin \theta } \\ \ & = \frac{\frac{\cos \theta}{\cos \theta} - \frac{ \sin \theta }{\cos \theta} }{\frac{\cos \theta}{\cos \theta} + \frac{\sin \theta}{\cos \theta} } \\ \ & = \frac{1-\tan \theta }{1+\tan \theta } \\ \ & = \text{ RHS } \\ \end{align} [/math][br][br]6. (g) [math] \frac{\sin \theta + \sin 2\theta}{1+\cos \theta + \cos 2\theta} = \tan \theta [/math][br]Solution:[br][math] \begin{align} \text{ LHS } & = \frac{\sin \theta + \sin 2\theta}{1+\cos \theta + \cos 2\theta} \\ \ & = \frac{ \sin \theta + 2\sin \theta \cos \theta }{ 1+ \cos \theta + 2\cos^2 \theta -1} \\ \ & = \frac{ \sin \theta (1+2\cos \theta)}{\cos \theta ( 1+2\cos \theta )} \\ \ & = \frac{ \sin \theta }{\cos \theta }\\ \ & = \tan \theta \\ \ & = \text { RHS } \\ \end{align} [/math][br][br]6. (h) [math] \frac{1+ \cos \beta + \cos 2\beta} {\sin \beta + \sin 2\beta } = \cot \beta [/math][br]Solution:[br][math] \begin{align} \text{ LHS } & = \frac{ 1+ \cos \beta + \cos 2\beta }{\sin \beta + \sin 2\beta}\\ \ & =\frac{1+\cos \beta + 2\cos^2 \beta-1}{\sin \beta+2\sin \beta \cos \beta }\\ \ & = \frac{\cos \beta( 1+ 2\cos \beta)}{\sin \beta(1+2\cos \beta)}\\ \ & = \frac{\cos \beta }{\sin \beta }\\ \ & = \cot \beta \\ \ & = \text{ RHS } \end{align} [/math][br][br]6. (i) [math] \frac{1-\sin 2\alpha}{\cos 2\alpha} = \frac{ 1-\tan \alpha}{1+\tan \alpha} = \tan (45^{\circ} - \alpha ) [/math][br]Solution:[br][math] \begin{align} \text{ LHS } & = \frac{1-\sin 2\alpha}{\cos 2\alpha} \\ \ & = \frac{\sin^2 \alpha + \cos^2 \alpha -2\sin \alpha \cos \alpha}{\cos^2\alpha -\sin^2 \alpha}\\ \ & =\frac{(\cos \alpha - \sin \alpha )^2}{(\cos \alpha -\sin \alpha)(\cos \alpha + \sin \alpha)} \\ \ & = \frac{\cos \alpha - \sin \alpha }{\cos \alpha + \sin \alpha }\\ \ & = \frac{\frac{\cos \alpha }{\cos \alpha}- \frac{\sin \alpha }{\cos \alpha}}{\frac{\cos \alpha}{\cos \alpha} + \frac{\sin \alpha }{\cos \alpha}}\\ \ & = \frac{1-\tan \alpha }{1+ \tan \alpha } = \text{ Mid Term } \\ \ & = \frac{ \tan 45^{\circ} - \tan \alpha } { 1+ \tan 45^{\circ} \tan \alpha } \\ \ & = \tan( 45^{\circ} - \alpha)\\ \ & = \text{ RHS } \end{align}[/math] [br][br]6. (j) [math] \tan \theta + \cot \theta = 2\text{cosec} 2\theta [/math][br]Solution:[br][math] \begin{align} \text{LHS } & = \tan \theta+ \cot \theta \\ \ & = \frac{\sin \theta }{\cos \theta}+\frac{\cos \theta}{\sin \theta}\\ \ & = \frac{\sin^2 \theta+\cos^2 \theta}{\cos \theta \sin \theta}\\ \ & = \frac{1}{\sin \theta \cos \theta}\times \frac{2}{2} \\ \ & = \frac{2}{2\sin \theta \cos \theta }\\ \ & = \frac{2}{\sin 2\theta} \\ \ & = 2 \text{ cosec } \theta \\ \ & = \text {RHS} \end{align} [/math][br][br]6. (k) [math] \text{cosec } 2A - \cot 2A = \tan A [/math][br]Solution:[br][math] \begin{align} \text{LHS } & = \text{ cosec } 2A-\cot 2A \\ \ & = \frac{1}{\sin 2A}-\frac{\cos 2A}{\sin 2A}\\ \ & =\frac{1- \cos 2A}{\sin 2A} \\ \ & = \frac{1-(1-2\sin^2 A)}{2\sin A \cos A}\\ \ & = \frac{1-1+2\sin^2 A}{2\sin A \cos A}\\ \ & =\frac{2\sin^2 A}{2\sin A \cos A}\\ \ & =\frac{\sin A}{\cos A }\\ \ & = \tan A \\ \ & = \text{ RHS }\\ \end{align}[/math][br][br]7. (a) [math] \tan(45^{\circ} + \theta) = \sec 2\theta + \tan 2\theta [/math][br]Solution:[br][math] \begin{align} \text{LHS } & = \tan (45^{\circ} + \theta) \\ \ & = \frac{\tan 45^{\circ} + \tan \theta}{1-\tan 45^{\circ} \tan \theta}\\ \ & = \frac{1+\tan \theta}{1-1\times \tan \theta }\\ \ & = \frac{1+\tan \theta}{1- \tan \theta }\\ \ & = \frac{1+\frac{\sin \theta}{\cos\theta}}{1- \frac{\sin \theta}{\cos \theta} }\\ \ & = \frac{\frac{\cos \theta + \sin \theta }{\cos \theta}}{\frac{\cos \theta - \sin \theta }{\cos \theta}}\\ \ & = \frac{\cos \theta + \sin \theta}{\cos \theta - \sin \theta }\\ \ & = \frac{\cos \theta + \sin \theta}{\cos \theta - \sin \theta } \times \frac{\cos \theta + \sin \theta}{\cos \theta + \sin \theta }\\ \ & = \frac{(\cos \theta + \sin \theta )^2 }{\cos^2 \theta - \sin^2 \theta }\\ \ & = \frac{ \cos^2 \theta + 2\cos \theta \sin \theta + \sin^2 \theta } {\cos 2\theta}\\ \ & = \frac{ \sin^2 \theta + \cos^2 \theta + 2\sin \theta \cos \theta }{ \cos 2\theta} \\ \ & = \frac{ 1+ \sin 2\theta } { \cos 2\theta} \\ \ & = \frac{ 1}{\cos 2\theta} + \frac{ \sin 2\theta}{\cos 2\theta}\\ \ & = \sec 2\theta + \tan 2\theta \\ \ & = \text{ RHS} \end{align} [/math][br][br]7. (b) [math] 1 -\sin 2A = 2 \sin^2 (45^{\circ} - A) [/math][br]Solution:[br][math] \begin{align} \text{RHS } \ & = 2\sin^2(45^{\circ}-A) \\ \ & =2\times\frac{1-\cos2(45^{\circ}-A)}{2}\\ \ & [\because \sin^2 \theta = \frac {1-\cos 2\theta}{2} ]\\ \ & = 1- \cos ( 90^{\circ} - 2A) \\ \ & = 1-\sin 2A \\ \ & = \text{ LHS }\\ \end{align} [/math][br][br]7. (c) [math] 2\cos^2 (45^{\circ} -\theta ) = 1+ \sin 2\theta [/math][br]Solution:[br][math] \begin{align} \text{ LHS } & = 2 \cos^2 (45^{\circ} -\theta)\\ \ & = 2 \times \frac{1+\cos 2(45^{\circ}-\theta)}{2}\\ \ & \left[ \because \cos^2 A = \frac{ 1+\cos 2A}{2} \right]\\ \ & = 1+\cos(90^{\circ} -2\theta)\\ \ & = 1+\sin 2\theta\\ \ & = \text{ RHS} \end{align} [/math][br][br]7. (d) [math] \cos^2 ( 45^{\circ} -A) -\sin^2 (45^{\circ} -A) = \sin 2A [/math][br]Solution:[br][math] \begin{align}\text{LHS } & = \cos^2 ( 45^{\circ} -A) -\sin^2 (45^{\circ} -A)\\ \ & = \cos 2(45^{\circ} - A) \\ \ & = \cos (90^{\circ} - 2A) \\ \ & = \sin 2A \\ \ & = \text { RHS }\end{align}[/math][br][br]7. (e) [math] \tan (A + 45^{\circ}) - \tan ( A - 45^{\circ}) = \frac{2(1+\tan^2 A)}{1-\tan^2 A} [/math][br]Solution[br][math] \begin{align}\text{LHS }\ & = \tan(A+45^{\circ}-\tan (A-45^{\circ}) \\ \ & =\frac{\tan A+\tan45^{\circ}}{1-\tan A\tan45^{\circ}}-\frac{\tan A-\tan45^{\circ}}{1+\tan A\tan45^{\circ}}\\ \ & = \frac{\tan A+1}{1-\tan A \times 1}- \frac{\tan A-1}{1+\tan A \times 1}\\ \ & =\frac{\tan A+1}{1-\tan A}-\frac{\tan A-1}{1+\tan A}\\ \ & =\frac{ (\tan A+1) (1+\tan A) -( \tan A-1)(1-\tan A)}{(1-\tan A)(1+\tan A) } \\ \ & = \frac{\tan A+\tan^2 A+1+\tan A - (\tan A -\tan^2 A -1+\tan A)}{1^2-\tan^2 A} \\ \ & =\frac{\tan A+\tan^2 A+1+\tan A- \tan A + \tan^2 A+1 -\tan A}{1-\tan^2 A}\\ \ & =\frac{2+2\tan^2 A}{1-\tan^2 A} \\ \ & =\frac{2\left(1+\tan^2A\right)}{1-\tan^2A}\\ \ & = \text{ RHS } \\ \end{align} [/math][br][br]7. (f) [math] \frac{1+\tan^2 (45^{\circ}-\theta )}{1-\tan^2 (45^{\circ}-\theta )} = \text{ cosec } 2\theta [/math][br]Solution:[br][math] \begin{align} \text{LHS } \ & = \frac{1+\tan^2 (45^{\circ}-\theta )}{1-\tan^2 (45^{\circ}-\theta )}\\ \ & = { \displaystyle \frac{1}{\frac{1-\tan^2(45^{\circ}-\theta)}{1+\tan^2(45^{\circ}-\theta)}} }\\ \ & = {\cos 2(45^{\circ}-\theta ) } \\ \ & = \frac{1}{\cos (90^{\circ} - 2\theta} ) \\ \ & = \frac{1}{\sin 2\theta } \\ \ & = \text{cosec } 2\theta \\ \ & =\text{ RHS } \end{align} [/math][br][br]8. (a) If [math] \cos\theta=\frac{1}{2}\left(a+\frac{1}{a}\right)[/math] then prove that: [math]\cos2\theta=\frac{1}{2}\left(a^2+\frac{1}{a^2}\right).[/math][br]Solution:[br][math] \begin{align} \text{LHS } &=\cos2\theta\\ \ &=2\cos^2\theta-1\\ \ &=2\left(\cos\theta\right)^2-1\\ \ &=2\left\{\frac{1}{2}\left(a+\frac{1}{a}\right)\right\}^2-1\\ \ &=2\times\frac{1}{4}\left(a+\frac{1}{a}\right)^2-1\\ \ &=\frac{1}{2}\left(a+\frac{1}{a}\right)^2-1\\ \ &=\frac{1}{2}\left(a^2+2\times a\times\frac{1}{a}+\frac{1}{a^2}\right)-1\\ \ &=\frac{1}{2}\left(a^2+\frac{1}{a^2}+2\right)-1\\ \ &=\frac{1}{2}\left(a^2+\frac{1}{a^2}\right)+\frac{1}{2}\times2-1\\ \ &=\frac{1}{2}\left(a^2+\frac{1}{a^2}\right)+1-1\\ \ &=\frac{1}{2}\left(a^2+\frac{1}{a^2}\right)\\ \ &= \text{ RHS }\\ \end{align} [/math][br][br]8. (b) If [math]\displaystyle\sin\theta=\frac{1}{2}\left(b+\frac{1}{b}\right)[/math][br] Prove that:[math]\displaystyle \cos2\theta=-\frac{1}{2}\left(b^2+\frac{1}{b^2}\right)[/math][br][math] \begin{align} \text{LHS } \ & \displaystyle =\cos2\theta\\ \ & \displaystyle=1-2\sin^2\theta\\ \ & \displaystyle =1-2\left(\sin\theta\right)^{^2}\\ \ & \displaystyle =1-2\left\{\frac{1}{2}\left(b+\frac{1}{b}\right)\right\}^2\\ \ & \displaystyle =1-2\times\frac{1}{4}\left(b+\frac{1}{b}\right)^2\\  \ & \displaystyle =1-\frac{1}{2}\left(b^2+2\times b\times\frac{1}{b}+\frac{1}{b^2}\right)\\ \ & \displaystyle =1-\frac{1}{2}\left(b^2+2+\frac{1}{b^2}\right)\\ \ & \displaystyle =1-\frac{1}{2}\left(b^2+\frac{1}{b^2}+2\right)\\ \ & \displaystyle =1-\frac{1}{2}\left(b^2+\frac{1}{b^2}\right)-\frac{1}{2}\times2\\ \ & \displaystyle =1-\frac{1}{2}\left(b^2+\frac{1}{b^2}\right)-1\\ \ & \displaystyle =-\frac{1}{2}\left(b^2+\frac{1}{b^2}\right)\\ \ & \displaystyle =\text{ RHS } \end{align} [/math][br][br]8. (c) If [math]\sin\beta=\frac{1}{2}\left(k+\frac{1}{k}\right)[/math] , show that [math] \sin3\beta=-\frac{1}{2}\left(k^3+\frac{1}{k^3}\right)[/math][br]Solution:[br][math] \begin{align} \text{LHS } \ & =\sin3\beta\\ \ & =3\sin\beta-4\sin^3\beta\\  \ & =3\times\frac{1}{2}\left(k+\frac{1}{k}\right)-4\times\left\{\frac{1}{2}\left(k+\frac{1}{k}\right)\right\}^3\\  \ & =\frac{3}{2}\left(k+\frac{1}{k}\right)-4\times\frac{1}{8}\left(k+\frac{1}{k}\right)^3\\ [br]\ & =\frac{3}{2} \left( k + \frac{1}{k} \right) - \frac{1}{2} \left(k+\frac{1}{k}\right)^3\\ [br]\ & =\frac{3}{2} \left( k + \frac{1}{k} \right) - \frac{1}{2} \left\{k^3+ \frac{1}{k^3}+3\times k\times \frac{1}{k} \left( 1+ \frac{1}{k} \right) \right\}\\ [br]\ & =\frac{3}{2} \left( k + \frac{1}{k} \right) - \frac{1}{2} \left\{k^3+ \frac{1}{k^3}+3 \left( k + \frac{1}{k} \right) \right\}\\ [br]\ & =\frac{3}{2} \left( k + \frac{1}{k} \right) - \frac{1}{2} \left(k^3+ \frac{1}{k^3}\right) - \frac{3}{2} \left( k+ \frac{1}{k} \right) \\ [br]\ & = - \frac{1}{2} \left(k^3+ \frac{1}{k^3}\right) \\ [br] \ & =\text{ RHS}\\ \end{align} [/math][br]Alternative[br][math] \begin{align} \text{LHS } \ & =\sin3\beta\\ \ & =3\sin\beta-4\sin^3\beta\\  \ & =3\times\frac{1}{2}\left(k+\frac{1}{k}\right)-4\times\left\{\frac{1}{2}\left(k+\frac{1}{k}\right)\right\}^3\\  \ & =\frac{3}{2}\left(k+\frac{1}{k}\right)-4\times\frac{1}{8}\left(k+\frac{1}{k}\right)^3\\  \ & =\frac{1}{2}\left\{3\left(k+\frac{1}{k}\right)-\left(k+\frac{1}{k}\right)^3\right\}\\   \ & =-\frac{1}{2}\left\{\left(k+\frac{1}{k}\right)^3-3\left(k+\frac{1}{k}\right)\right\}\\ \ & =-\frac{1}{2}\left\{\left(k+\frac{1}{k}\right)^3-3\times k\times\frac{1}{k}\left(a+\frac{1}{k}\right)\right\}\\ \ & =-\frac{1}{2}\left(k^3+\frac{1}{k^3}\right) \left[\because k^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)\right]\\ \ & =\text{ RHS}\\ \end{align} [/math][br][br]9. (a) [math] (\cos 2A -\cos 2B)^2 + (\sin 2A + \sin 2B)^2 = 4\sin^2 (A+B) [/math][br]Solution:[br][math]\begin{align} \text{LHS } & = (\cos 2A -\cos 2B)^2 + (\sin 2A + \sin 2B)^2 \\ \ & = \cos^2 2A -2\cos 2A \cos 2B + \cos ^2 2B + \sin^2 2A +2\sin 2A \sin 2B + \sin^2 2B \\ \ & = \sin^2 2A + \cos^2 2A + \sin^2 2B+ \cos^2 2B -2(\cos 2A \cos 2B - \sin 2A \sin 2B) \\ \ & = 1+1-2\cos (2A+2B) \\ \ & = 2 -2\cos (2A+2B) \\ \ & = 2 -2\cos 2(A+B) \\ \ & = 2 - 2\{ 1-2\sin^2 (A+B) \}\\ \ & = 2 -2+4\sin^2(A+B)\\ \ & = 4\sin^2(A+B)\\ \ & = \text{ RHS } \end{align} [/math][br][br]9. (b) [math] (\sin 2A - \sin 2B)^2 + (\cos 2A + \cos 2B)^2 = 4\cos^2(A+B) [/math][br]Solution:[br][math] \begin{align} \text{LHS } & =(\sin 2A - \sin 2B)^2+(\cos 2A +\cos 2B)^2 \\ \ & = \sin^2 2A -2\sin 2A \sin 2B + \sin^2 2B +\cos^2 2A +2\cos 2A \cos 2B + \cos ^2 2B \\ \ & = \sin^2 2A + \cos^2 2A + \sin^2 2B+ \cos^2 2B + 2(\cos 2A \cos 2B - \sin 2A \sin 2B) \\ \ & = 1+1+2\cos (2A+2B) \\ \ & = 2 +2\cos (2A+2B) \\ \ & = 2 +2\cos 2(A+B) \\ \ & = 2 +2\{ 2\cos^2 (A+B)-1 \}\\ \ & = 2 +4\cos^2(A+B)-2\\ \ & = 4\cos^2(A+B)\\ \ & = \text{ RHS } \end{align}[/math][br][br]10. (a) Prove that: [math] \cos^2\theta+\sin^2\theta.\cos2\alpha=\cos^2\alpha+\sin^2\alpha.\cos2\theta[/math][br]Solution:[br][math] \begin{align} \text{ LHS} \ & =\cos^2\theta+\sin^2\theta.\cos2\alpha\\ \ & =\cos^2\theta+\sin^2\theta\left(1-2\sin^2\alpha\right)\\ \ & =\cos^2\theta+\sin^2\theta-2\sin^2\theta\sin^2\alpha\\ \ & =1-2\sin^2\theta\sin^2\alpha\\ \ & =\cos^2\alpha+\sin^2\alpha-2\sin^2\theta\sin^2\alpha\\ \ & =\cos^2\alpha+\sin^2\alpha\left(1-2\sin^2\theta\right)\\ \ & =\cos^2\alpha+\sin^2\alpha\cos2\theta\\ \ & = \text{ RHS}\\ \end{align} [/math][br][br]10. (b) [math] (1+\cos 2\theta + \sin 2\theta )^2 =4\cos^2 \theta(1+\sin 2\theta) [/math][br]Solution:[br][math] \begin{align} \text{LHS} & = (1+\cos 2\theta + \sin 2\theta )^2 =4\cos^2 \theta(1+\sin 2\theta)\\ \ & = ( 1+ 2\cos^2 \theta -1 + 2\sin \theta \cos \theta )^2\\ \ & = (2\cos^2 \theta + 2\sin \theta \cos \theta)^2 \\ \ & = \{ 2\cos \theta(\cos \theta + \sin \theta ) \}^2\\ \ & = 4\cos^2 \theta ( \cos \theta +\sin \theta)^2 \\ \ & = 4\cos^2 \theta (\cos^2 \theta + 2\cos \theta \sin \theta + \sin^2 \theta )\\ \ & = 4\cos^2 \theta ( \sin^2 \theta + \cos^2 \theta + 2\cos \theta \sin \theta )\\ \ & = 4\cos^2 \theta (1+\sin 2\theta)\\ \ & = \text { RHS} \end{align} [/math][br][br]10. (c) Prove that: [math](2\cos A+1)(2\cos A-1)\left(2\cos2A-1\right)=1+ 2\cos4A[/math][br]Solution:[br][math] \begin{align} \text{LHS} \ & =(2\cos A+1)(2\cos A-1)\left(2\cos2 A-1\right)\\ \ & =\left\{\left(2\cos A\right)^2-1^2\right\}\left(2\cos2 A-1\right)\\ \ & =\left(4\cos^2 A-1\right)\left(2\cos2 A-1\right)\\ \ & =\left(4\times\frac{1+\cos2 A}{2}-1\right)\left(2\cos2 A-1\right)\\ \ & =\left(2+2\cos2 A-1\right)\left(2\cos2 A-1\right)\\ \ & =\left(2\cos2 A+1\right)\left(2\cos2 A-1\right)\\ \ & =\left(2\cos2 A\right)^2-1^2\\ \ & =4\cos^22 A-1\\ \ & =4\times\frac{1+\cos4 A}{2}-1\\ \ & =2\left(1+\cos4 A\right)-1\\ \ & =2+2\cos4 A-1\\ \ & =1+ 2\cos4 A\\ \ & = \text{ RHS }\\ \end{align} [/math][br][br]10. (d) [math] 1+\cos 8 \theta = ( 2\cos 4\theta -1 ) (2\cos 2\theta -1)( 2\cos \theta -1) (2\cos \theta +1) [/math][br]Solution:[br][math]\begin{align} \text{RHS} \ & = (2\cos 4\theta-1)(2\cos 2\theta -1) ( 2\cos 2\theta -1)(2\cos \theta +1)\\ \ & = (2\cos 4\theta-1)(2\cos 2\theta -1)\left\{(2\cos 2\theta )^2 -1^2 \right\}\\ \ & = (2\cos 4\theta-1)(2\cos 2\theta -1)(4\cos^2\theta -1^2 )\\ \ & = (2\cos 4\theta-1)(2\cos 2\theta -1) \left( 4\times \frac{1+\cos 2\theta}{2} -1\right)\\ \ & = (2\cos 4\theta-1)(2\cos 2\theta -1) (2+2\cos 2\theta - 1)\\ \ & = (2\cos 4\theta-1)(2\cos 2\theta -1) (2\cos 2\theta +1 ) \\ \ & = (2\cos 4\theta -1 ) \{ (2\cos 2\theta)^2 -1^2 \}\\ \ & = (2\cos 4\theta -1 ) (4\cos^2 2\theta-1)\\ \ & = (2\cos 4\theta -1 )\left( 4\times \frac{1+\cos 4\theta}{2}-1 \right) \\ \ & = (2\cos 4\theta -1 ) ( 2+ 2\cos 4\theta -1 ) \\ \ & = ( 2\cos 4\theta -1 ) ( 2\cos 4\theta +1)\\ \ & = (2\cos 4\theta )^2 -1^2\\ \ & = 4\cos^2 4 \theta -1\\ \ & = 4 \times \frac{1+\cos 8 \theta}{2} -1\\ \ & = 2+2\cos 8 \theta -1\\ \ & = 1+\cos 8 \theta\\ \ & = \text{ LHS }\\ \end{align} [/math][br][br]11. (a) Prove that: [math]\cos^6\theta-\sin^6\theta=\frac{1}{4}\left(\cos^32\theta+3\cos2\theta\right)[/math][br]Solution:[br][math] \begin{align} \text{LHS } \ & =\cos^6\theta-\sin^6\theta\\ \ & =\left(\cos^2\theta\right)^3-\left(\sin^2\theta\right)^3\\ \ & =\left(\cos^2\theta-\sin^2\theta\right)\left\{\left(\cos^2\theta\right)^2+\cos^2\theta\sin^2\theta+\left(\sin^2\right)^2\right\}\\\ & =\cos2\theta\left\{\left(\cos^2\theta\right)^2+2\cos^2\theta\sin^2\theta+\left(\sin^2\right)^2-\cos^2\theta\sin^2\theta\right\}\\ \ & =\cos2\theta\left\{\left(\cos^2\theta+\sin^2\theta\right)^2-\frac{1}{4}\left(2\sin\theta\cos\theta\right)^2\right\}\\ \ & =\cos2\theta\left\{\left(1\right)^2-\frac{1}{4}\left(\sin2\theta\right)^2\right\}\\ \ & =\cos2\theta\left\{1-\frac{1}{4}\sin^22\theta\right\}\\ \ & =\cos2\theta\left\{\frac{4-\sin^22\theta}{4}\right\}\\ \ & =\cos2\theta\left\{\frac{4-\left(1-\cos^22\theta\right)}{4}\right\}\\ \ & =\cos2\theta\left(\frac{4-1+\cos^22\theta}{4}\right)\\ \ & =\cos2\theta\left(\frac{3+\cos^22\theta}{4}\right)\\ \ & =\frac{3\cos2\theta+\cos^32\theta}{4}\\ \ & =\frac{1}{4}\left(\cos^32\theta+3\cos2\theta\right)\\ \ & = \text{ RHS }\\ \end{align} [/math][br] [br]11. (b) Prove that: [math]\cos^6\theta+\sin^6\theta=\frac{1}{8}\left(5+3\cos4\theta\right)[/math][br]Solution:[br][math] \begin{align} \text{LHS } \ & =\cos^6\theta+\sin^6\theta\\ \ & =\left(\cos^2 \theta \right)^3+\left(\sin^2\theta \right)^3\\ \ & =\left(\sin^2\theta+\cos^2\theta\right)\left\{\left(\cos^2\right)^2-\cos^2\theta\sin^2\theta+\left(\sin^2\theta\right)^2\right\}\\ \ & =\left(1\right)\left\{\left(\cos^2\theta\right)^2+2\cos^2\theta\sin^2\theta+\left(\sin^2\theta\right)^2-3\cos^2\theta\sin^2\theta\right\}\\ \ & =\left\{\left(\cos^2\theta+\sin^2\theta\right)^2-\frac{3}{4}\left(2\cos\theta\sin\theta\right)^2\right\}\\ \ & =\left(1\right)^2-\frac{3}{4}\left(\sin2\theta\right)^2\\ \ & =1-\frac{3}{4}\sin^22\theta\\ \ & =1-\frac{3}{4}\times\frac{1-\cos4\theta}{2}\\ \ & =\frac{8-3+3\cos4\theta}{8}\\ \ & =\frac{5+3\cos4\theta}{8}\\ \ & =\frac{1}{8}\left(5+3\cos4\theta\right)\\ \ & = \text{ RHS}\\ \end{align} [/math][br][br]11. (c) Prove that: [math]\cos^8\theta+\sin^8\theta=1-\sin^22\theta+\frac{1}{8}\sin^42\theta[/math][br]Solution:[br][math]\begin{align} \text{LHS } \ & =\cos^8\theta+\sin^8\theta\\ \ & =\left(\cos^4\theta\right)^2+\left(\sin^4\theta\right)^2\\ \ & =\left(\cos^4\theta-\sin^4\theta\right)^2+2\cos^4\theta\sin^4\theta\\ \ & =\left\{\left(\cos^2\theta\right)^2-\left(\sin^2\theta\right)^2\right\}^2+\frac{2^4}{2^3}\cos^4\theta\sin^4\theta\\ \ & =\left\{\left(\cos^2\theta+\sin^2\theta\right)\left(\cos^2\theta-\sin^2\theta\right)\right\}^2 +\frac{1}{8}\left(2\sin\theta\cos\theta\right)^4\\ \ & =\left\{1\times\cos2\theta\right\}^2+\frac{1}{8}\left(\sin2\theta\right)^4\\ \ & =\cos^22\theta+\frac{1}{8}\sin^42\theta\\ \ & =1-\sin^22\theta+\frac{1}{8}\sin^42\theta\\ \ & = \text{ RHS} \end{align} [/math][br][br]11. (d) Prove that: [math]\frac{1}{\sin10^\circ}-\frac{\sqrt{3}}{\cos10^\circ}[/math][br]Solution:[br][math]\begin{align} \text{LHS } \ & =\frac{1}{\sin10^\circ}-\frac{\sqrt{3}}{\cos10^\circ}\\ \ & =\frac{\cos10^\circ-\sqrt{3}\sin10^\circ}{\sin10^\circ\cos10^\circ}\\ \ & =\frac{\frac{1}{2}\cos10^\circ-\frac{\sqrt{3}}{2}\sin10^\circ}{\frac{1}{2}\sin10^\circ\cos10^\circ}\\ \ & =\frac{\sin30^\circ\cos10^\circ-\cos30^\circ\sin10^\circ}{\frac{1}{2}\sin10^\circ\cos10^\circ}\\ \ & =\frac{\sin\left(30^\circ-10^\circ\right)}{\frac{1}{2}\sin10^\circ\cos10^\circ}\\ \ & =\frac{\sin20^\circ}{\frac{1}{2}\sin10^\circ\cos10^\circ}\\ \ & =\frac{2\sin10^\circ\cos10^\circ}{\frac{1}{2}\sin10^\circ\cos10^\circ}\\ \ & =\frac{2}{\frac{1}{2}}\\ \ & =2\times2\\ \ & =4\\ \ & = \text{ RHS}\\ \end{align} [/math] [br][br]11. (e) Prove that: [math]\sqrt{3}\text{cosec }40^{\circ}+\sec40^{\circ}=4[/math][br]Solution:[br][math] \begin{align} \text{LHS } \ & =\sqrt{3}\text{cosec }40^\circ+\sec40^\circ\\ \ & =\frac{\sqrt{3}}{\sin40^\circ}+\frac{1}{\cos40^\circ}\\ \ & =\frac{\sqrt{3}\cos40^\circ+\sin40^\circ}{\sin40^\circ\cos40^\circ}\\ \ & =\frac{\frac{\sqrt{3}}{2}\cos40^\circ+\frac{1}{2}\sin40^\circ}{\frac{1}{2}\sin40^\circ\cos40^\circ}\\ \ & =\frac{\sin60^\circ\cos40^\circ+\cos60^\circ\sin60^\circ}{\frac{1}{2}\sin40^\circ\cos40^\circ}\\ \ & =\frac{\sin100^\circ}{\frac{1}{2}\sin40^\circ\cos40^\circ}\\ \ & =\frac{\sin\left(180^\circ-80^\circ\right)}{\frac{1}{2}\sin40^\circ\cos40^\circ}\\ \ & =\frac{\sin80^\circ}{\frac{1}{2}\sin40^\circ\cos40^\circ}\\ \ & =\frac{2\sin40^\circ\cos40^\circ}{\frac{1}{2}\sin40^\circ\cos40^\circ}\\ \ & =2\times2\\ \ & =4\\ \ & = \text{ RHS } \end{align} [/math][br][br]11. (f) Prove that:[math]\sqrt{3}\text{cosec }20^{\circ}-\sec20^{\circ}=4[/math][br]Solution:[br][math] \begin{align} \text{ LHS } = \ & =\sqrt{3}\text{cosec }20^{\circ}-\sec20^{\circ}\\ \ & =\frac{\sqrt{3}}{\sin20^\circ}-\frac{1}{\cos20^\circ}\\ \ & =\frac{\sqrt{3}\cos20^\circ-\sin20^\circ}{\sin20^\circ\cos20^\circ}\\ \ & =\frac{\frac{\sqrt{3}}{2}\cos20^\circ-\frac{1}{2}\sin20^\circ}{\frac{1}{2}\sin20^\circ\cos20^\circ}\\ \ & =\frac{\sin60^\circ\cos20^\circ-\cos60^\circ\sin20^\circ}{\frac{1}{2}\sin20^\circ\cos20^\circ}\\ \ & =\frac{\sin\left(60^\circ-20^\circ\right)}{\frac{1}{2}\sin20^\circ\cos20^\circ}\\ \ & =\frac{\sin40^\circ}{\frac{1}{2}\sin20^\circ\cos20^\circ}\\ \ & =\frac{2\sin20^\circ\cos20^\circ}{\frac{1}{2}\sin20^\circ\cos20^\circ}\\ \ & =\frac{2}{\frac{1}{2}}\\ \ & =4\\ \ & = \text{ RHS } \end{align} [/math] [br][br]12. (a) [math] \frac{1}{\sin 2A} + \frac{ \cos 4A}{\sin 4A} = \cot A - \text{cosec } 4A [/math][br]Solution:[br][math]\begin{align} \text{LHS } & = \frac{1}{\sin 2A} + \frac{ \cos 4A}{\sin 4A} \\ \ & = \frac{1}{\sin 2A} + \frac{ 2\cos^2 2A -1}{2\sin 2A \cos 2A} \\ \ & = \frac{2\cos 2A + 2\cos^2 2A -1 }{2\sin 2A \cos 2A} \\ \ & = \frac{ 2\cos 2A(1+\cos 2A) - 1}{2\sin 2A \cos 2A } \\ \ & = \frac{2\cos 2A (1+\cos 2A}{2\sin 2A \cos 2A} - \frac{1}{2\sin 2A \cos 2 A }\\ \ & = \frac{ 1+\cos 2A}{\sin 2A} - \frac{1}{\sin 4A} \\ \ & = \frac{ 1+ 2\cos^2 A -1}{2\sin A \cos A} - \text{cosec } 4A\\ \ & = \frac{2\cos^2 A }{2\sin A \cos A} -\text{cosec } 4A\\ \ & = \frac{ \cos A } {\sin A} -\text{cosec } 4A\\ \ & = \cot A - \text{cosec } 4A\\ \ & = \text{ RHS } \\ \end{align} [/math][br][br]12. (b)[math] \cot 8A +\text{cosec } 4A = \cot 2A - \text{cosec }8A [/math][br]Soluion:[br][math] \begin{align} \text{LHS } & = \cot 8A +\text{cosec } 4A\\[br]\ & = \frac{\cos 8A}{\sin 8A}+\frac{1}{\sin 4A}\\ [br]\ & = \frac{2\cos^2 4A-1 }{2\sin 4A \cos 4A}+\frac{1}{\sin 4A}\\ [br]\ & = \frac{2\cos^2 4A-1+2\cos 4A}{2\sin 4A \cos 4A}\\[br]\ & = \frac{2\cos^2 4A+2\cos 4A-1}{2\sin 4A \cos 4A}\\ [br]\ & = \frac{2\cos 4A(\cos 4A+1)-1}{2\sin 4A \cos 4A}\\ [br]\ & = \frac{2\cos 4A(\cos 4A+1)}{2\sin 4A \cos 4A} -\frac{1}{2\sin 4A \cos 4A}\\[br]\ & = \frac{\cos 4A+1}{\sin 4A } -\frac{1}{\sin 8A}\\[br]\ & = \frac{2\cos^2 2A-1+1}{2\sin 2A \cos 2A } -\text{cosec }{8A}\\[br]\ & = \frac{2\cos^2 2A}{2\sin 2A \cos 2A } -\text{cosec }{8A}\\ [br]\ & = \frac{\cos 2A}{\sin 2A } -\text{cosec }{8A}\\ [br]\ & = \cot 2A -\text{cosec }{8A}\\[br]\ & =\text{RHS} \end{align} [/math][br][br]12. (c) Prove that: [math] \frac{\sec4\theta-1}{\sec2\theta-1}=\tan4\theta\cot\theta [/math][br]Solution:[br][math]\begin{align}\text{LHS} & =\frac{\sec4\theta-1}{\sec2\theta-1} \\ & = \dfrac{\dfrac{1}{\cos4\theta}-1}{\dfrac{1}{\cos2\theta}-1} \\  & = \dfrac{\dfrac{1-\cos4\theta}{\cos4\theta}}{\dfrac{1-\cos2\theta}{\cos2\theta}} \\ & =\frac{1-\cos4\theta}{\cos4\theta}\times\frac{\cos2\theta}{1-\cos2\theta} \\  & =\frac{1-\left(1-2\sin^22\theta\right)}{\cos4\theta}\times\frac{\cos2\theta}{1-\left(1-2\sin^2\theta\right)} \\  & =\frac{2\sin^22\theta}{\cos4\theta}\times\frac{\cos2\theta}{2\sin^2\theta} \\  & =\frac{2\sin2\theta\cos2\theta}{\cos4\theta}\times\frac{\sin2\theta}{2\sin^2\theta} \\  & =\frac{\sin4\theta}{\cos4\theta}\times\frac{2\sin\theta\cos\theta}{2\sin^2\theta} \\  & =\tan4\theta\times\frac{\cos\theta}{\sin\theta} \\  & =\tan4\theta.\cot\theta \\  & = \text{ RHS} \end{align}[/math][br][br]12. (d) Prove that: [math]\displaystyle \frac{\sec8A-1}{\sec4A-1}=\frac{\tan8A}{\tan2A} [/math][br]Solution:[br][math] \begin{align}\text{LHS } & =\frac{\sec8A-1}{\sec4A-1}\\ & = \dfrac{\dfrac{1}{\cos8A}-1}{\dfrac{1}{\cos4A}-1}\\  & = \dfrac{\dfrac{1-\cos8A}{\cos8A}}{\dfrac{1-\cos4A}{\cos4A}}\\  & =\frac{1-\cos8A}{\cos8A}\times\frac{\cos4A}{1-\cos4A}\\  & =\frac{1-\left(1-2\sin^24A\right)}{\cos8A}\times\frac{\cos4A}{1-\left(1-2\sin^2 2A\right)}\\  & =\frac{2\sin^24A}{\cos8A}\times\frac{\cos4A}{2\sin^2 2A}\\  & =\frac{2\sin4A\cos4A}{\cos8A}\times\frac{\sin4A}{2\sin^2 2A}\\  & =\frac{\sin8A}{\cos8A}\times\frac{2\sin2A\cos2A}{2\sin^2 2A}\\  \ & =\tan8A\times\frac{\cos2A}{\sin2A}\\  & =\tan8A.\cot2A\\ & = \tan 8A \times \frac{1}{\tan 2A}\\ & = \frac{\tan 8A}{\tan 2A} \\  & = \text{ RHS} \end{align} [/math] [br][br]12. (e) Prove that: [math] \tan\theta+2\tan2\theta+4\tan4\theta+8\cot8\theta=\cot\theta [/math][br]Solution:[br][math] \begin{align} \text{LHS } &=\tan\theta+2\tan2\theta+4\tan4\theta+8\cot8\theta\\ \ &=\tan\theta+2\tan2\theta+4\tan4\theta+\frac{8}{\tan8\theta}\\ \ &=\tan\theta+2\tan2\theta+4\tan4\theta+\frac{8}{\frac{2\tan4\theta}{1-\tan^24\theta}}\\ \ &=\tan\theta+2\tan2\theta+4\tan4\theta+\frac{8\left(1-\tan^24\theta\right)}{2\tan4\theta}\\ \ &=\tan\theta+2\tan2\theta+4\tan4\theta+\frac{4\left(1-\tan^24\theta\right)}{\tan4\theta}\\ \ &=\tan\theta+2\tan2\theta+\frac{4\tan^24\theta+4-4\tan^24\theta}{\tan4\theta}\\ \ &=\tan\theta+2\tan2\theta+\frac{4}{\tan4\theta}\\ \ &=\tan\theta+2\tan2\theta+\frac{4}{\frac{2\tan2\theta}{1-\tan^22\theta}}\\ \ &=\tan\theta+2\tan2\theta+\frac{4\left(1-\tan^22\theta\right)}{2\tan2\theta}\\ \ &=\tan\theta+2\tan2\theta+\frac{2\left(1-\tan^22\theta\right)}{\tan2\theta}\\ \ &=\tan\theta+2\tan2\theta+\frac{2-2\tan^22\theta}{\tan2\theta}\\ \ &=\tan\theta+\frac{2\tan^22\theta+2-2\tan^22\theta}{\tan2\theta}\\ \ &=\tan\theta+\frac{2}{\tan2\theta}\\ \ &=\tan\theta+\frac{2}{\frac{2\tan\theta}{1-\tan^2\theta}}\\ \ &=\tan\theta+\frac{2\left(1-\tan^2\theta\right)}{2\tan\theta}\\ \ &=\tan\theta+\frac{1-\tan^2\theta}{\tan\theta}\\ \ &=\frac{\tan^2\theta+1-\tan^2\theta}{\tan\theta}\\ \ &=\frac{1}{\tan\theta}\\ \ &=\cot\theta\\ \ &=\text{ RHS} \end{align} [/math][br][br]13. (a) Prove that: [br][math] 4\left(\cos^310^\circ+\sin^320^\circ\right)=3\left(\cos10^\circ+\sin20^\circ\right) [/math][br]Solution:[br][math] \begin{align} \text{LHS } \ & =4\left(\cos^310^\circ+\sin^320^\circ\right)\\ \ & =4\cos^310^\circ+4\sin^320^\circ\\ \ & =3\cos10^\circ+\cos3\left(10^\circ\right)+3\sin20^\circ-\sin3\left(20^\circ\right)\\ \ & =3\cos10^\circ+\cos30^\circ+3\sin20^\circ-\sin60^\circ\\ \ & =3\cos10^\circ+\frac{\sqrt{3}}{2}+3\sin20^\circ-\frac{\sqrt{3}}{2}\\ \ & =3\cos10^\circ+3\cos20^\circ\\ \ & =3\left(\cos10^\circ+\cos20^\circ\right)\\ \ & =\text{ RHS } \end{align} [/math][br] [br]13. (b) Prove that: [math] \sin^3\theta\cos3\theta+\cos^3\theta\sin3\theta=\frac{3}{4}\sin4\theta [/math][br]Solution:[br][math]\begin{align}\text{LHS } \ & =\sin^3\theta\cos3\theta+\cos^3\theta\sin3\theta\\ \ & =\frac{3\sin\theta-\sin3\theta}{4}\times\cos3\theta+\frac{3\cos\theta+\cos3\theta}{4}\times\sin3\theta\\ \ & =\frac{3\cos3\theta\sin\theta-\sin3\theta\cos3\theta}{4}+\frac{3\sin3\theta\cos\theta+\sin3\theta\cos3\theta}{4}\\ \ & =\frac{3\cos3\theta\sin\theta-\sin3\theta\cos3\theta+3\sin3\theta\cos\theta+\sin3\theta\cos3\theta}{4}\\ \ & =\frac{3\left(\cos3\theta\sin\theta+\sin3\theta\cos\theta\right)}{4}\\ \ & =\frac{3\sin\left(3\theta+\theta\right)}{4}\\ \ & =\frac{3}{4}\sin4\theta\\ \ & =\text{ RHS } \end{align} [/math][br][br]13. (c) Prove that:[math] \cos^3\theta\cos3\theta+\sin^3\theta\sin3A=\cos^32\theta[/math][br]Solution:[br][math] \begin{align} \text{LHS } \ & =\cos^3\theta.\cos3\theta+\sin^3\theta.\sin3\theta\\ \ & =\frac{3\cos\theta+\cos3\theta}{4}\times\cos3\theta+\frac{3\sin\theta-\sin3\theta}{4}\times\sin3\theta\\ \ & =\frac{3\cos3\theta\cos\theta+\cos^23\theta}{4}+\frac{3\sin3\theta\sin\theta-\sin^23\theta}{4}\\ \ & =\frac{3\cos3\theta\cos\theta+\cos^23\theta+3\sin3\theta\sin\theta-\sin^23\theta}{4}\\ \ & =\frac{3\left(\cos3\theta\cos\theta+\sin3\theta\sin\theta\right)+\left(\cos^23\theta-\sin^23\theta\right)}{4}\\ \ & =\frac{3\cos\left(3\theta-\theta\right)+\cos2\left(3\theta\right)}{4}\\ \ & =\frac{3\cos\left(3\theta-\theta\right)+\cos6\theta}{4}\\ \ & =\frac{3\cos2\theta+\cos3\left(2\theta\right)}{4}\\ \ & =\frac{3\cos2\theta+4\cos^3\theta-3\cos\theta}{4}\\ \ & =\frac{4\cos^3\theta}{4}\\ \ & =\cos^3\theta\\ \ & = \text{ RHS} \end{align} [/math][br][br]13. (d) Prove that: [math]\displaystyle \tan A + \tan \left(\frac{\pi^c}{3} \right) - \tan \left(\frac{\pi^c}{3} \right) [/math][br]Solution:[br][math] \begin{align}\text{ LHS} & =\tan A + \tan\left(\frac{\pi^c}{3}+A\right)-\tan \left(\frac{\pi^c}{3}-A\right)\\ \ &=\tan A + \tan\left(60^{\circ}+A\right)-\tan \left(60^{\circ}-A\right)\\ \ & = \tan A + \frac{\tan60^{\circ}+\tan A}{1-\tan 60^{\circ}\tan A} - \frac{\tan60^{\circ}-\tan A}{1+\tan 60^{\circ}\tan A}\\ \ & = \tan A+ \frac{\sqrt{3}+\tan A}{1-\sqrt{3}\tan A}- \frac{\sqrt{3}-\tan A}{1+\sqrt{3}\tan A}\\ \ & = \tan A+ \frac{(\sqrt{3}+\tan A)(1+\sqrt{3}\tan A)-(\sqrt{3}-\tan A)(1-\sqrt{3}\tan A)}{(1-\sqrt{3}\tan A)(1+\sqrt{3}\tan A)}\\ \ & = \tan A+\frac{\sqrt{3}+3\tan A+\tan A+\sqrt{3}\tan^2 A-(\sqrt{3}-3\tan A-\tan A+\sqrt{3}\tan^2 A)}{1^2 -(\sqrt{3}\tan A)^2 } \\ \ & = \tan A + \frac{\sqrt{3}+3\tan A+\tan A+\sqrt{3}\tan^2 A-\sqrt{3}+3\tan A+\tan A-\sqrt{3}\tan^2 A}{1-3\tan^2 A}\\ \ & = \tan A +\frac{8\tan A}{1-3\tan^2 A}\\ \ & = \frac{\tan A(1-3\tan^2 A)+8\tan A}{1-3\tan^2 A}\\ \ & = \frac{\tan A -3\tan^3 A+ 8 \tan A}{1-3\tan^2 A}\\ \ & =\frac{9\tan A -3\tan^3 A}{1-3\tan^2 A}\\ \ & =3\left(\frac{3\tan A -\tan^3 A}{1-3\tan^2 A}\right)\\ \ & = 3\tan 3A \\ \ & = \text{ RHS} \end{align} [/math][br][br]14 (i) If [math] 2 \tan A = 3\tan B [/math] prove that [math] \tan( A+ B)=\frac{5\sin2 B}{5\cos2 B-1} [/math][br]Solution:[br]Given,[br][math] \begin{align} 2\tan A & =3\tan B \\ or, \tan A & =\frac{3\tan B}{2} \end{align} [/math][br] Now,[br][math]\begin{align}\text{LHS } \ & =\tan\left( A+ B\right)\\ \ & =\frac{\tan A+\tan B}{1-\tan A\tan B}\\ \ & =\frac{\frac{3\tan B}{2}+\tan B}{1-\frac{3\tan B}{2}\times\tan B}\\ \ & =\frac{\frac{3\tan B+2\tan B}{2}}{\frac{2-3\tan^2 B}{2}}\\ \ & =\frac{5\tan B}{2-3\tan^2 B}\\ \ & =\frac{5\frac{\sin B}{\cos B}}{2-3\times\frac{\sin^2 B}{\cos^2 B}}\\ \ & =\frac{5\frac{\sin B}{\cos B}}{\frac{2\cos^2 B-3\sin^2 B}{\cos^2 B}}\\ \ & =\frac{5\sin B}{\cos B}\times\frac{\cos^2 B}{2\cos^2 B-3\sin^2 B}\\ \ & =\frac{5\sin B\cos B}{2\cos^2 B-3\sin^2 B}\times\frac{2}{2}\\ \ & =\frac{10\sin B\cos B}{4\cos^2 B-6\sin^2 B}\\ \ & =\frac{5\left(2\sin B\cos B\right)}{4\times\frac{1+\cos2 B}{2}-6\times\frac{1-\cos2 B}{2}}\\ \ & =\frac{5\sin2 B}{2+2\cos2 B-3+3\cos2 B}\\ \ & =\frac{5\sin2 B}{5\cos2 B-1}\\ \ & = \text{ RHS} \end{align} [/math] [br][br]14 (ii) [math] 2 \tan A = 3\tan B [/math] prove that: [math] \tan ( A - B ) = \frac {\sin 2 B }{5-\cos 2 B} [/math][br]Solution:[br]Given,[br][math] \begin{align}2\tan A &=3\tan B \\ \tan A & =\frac{3\tan B}{2} \end{align} [/math][br][math] \begin{align} \text{LHS } \ &=\tan\left( A- B\right) \\ \ &=\frac{\tan A-\tan B}{1+\tan A\tan B} \\ \ &=\frac{\frac{3\tan B}{2}-\tan B}{1+\frac{3\tan B}{2}\times\tan B} \\ \ &=\frac{\frac{3\tan B-2\tan B}{2}}{\frac{2-3\tan^2 B}{2}} \\ \ &=\frac{\tan B}{2+3\tan^2 B} \\ \ &=\frac{\frac{\sin B}{\cos B}}{2+3\times\frac{\sin^2 B}{\cos^2 B}} \\ \ &=\frac{\frac{\sin B}{\cos B}}{\frac{2\cos^2 B+3\sin^2 B}{\cos^2 B}} \\ \ &=\frac{\sin B}{\cos B}\times\frac{\cos^2 B}{2\cos^2 B+3\sin^2 B} \\ \ &=\frac{\sin B\cos B}{2\cos^2 B+3\sin^2 B}\times\frac{2}{2} \\ \ &=\frac{2\sin B\cos B}{4\cos^2 B+6\sin^2 B} \\ \ &=\frac{\sin2 B}{4\times\frac{1+\cos2 B}{2}+6\times\frac{1-\cos2 B}{2}} \\ \ &=\frac{\sin2 B}{2+2\cos2 B+3-3\sin2 B} \\ \ &=\frac{\sin2 B}{5-\cos2 B} \\ \ &= \text{ RHS} \end{align} [/math][br][br]15. (a) Prove that: [math] \sin^4 A=\frac{1}{8}\left(3-4\cos2 A+\cos4 A\right) [/math][br]Solution:[br][math] \begin{align} \text{LHS }  \ & =\sin^4 A \\  \ & =\left(\sin^2 A\right)^2 \\  \ & =\left(\frac{1-\cos2 A}{2}\right)^2 \\  \ & =\frac{1}{4}\left(1-\cos2 A\right)^2 \\  \ & =\frac{1}{4}\left(1^2-2\times1\times\cos2 A+\cos^22 A\right) \\  \ & =\frac{1}{4}\left(1-2\cos2 A+\frac{1+\cos4 A}{2}\right) \\  \ & =\frac{1}{4}\left(\frac{2-4\cos2 A+1+\cos4 A}{2}\right) \\  \ & =\frac{3-4\cos2 A+\cos4 A}{8} \\  \ & =\frac{1}{8}(3-4\cos2 A+\cos4 A) \\  \ & = \text{ RHS} \end{align} [/math][br][br]15. (b) Prove that: [math] \cos^4 A=\frac{1}{8}\left(3+4\cos2 A+\cos4 A\right)[/math][br]Solution:[br][math] \begin{align}\text{LHS}  \ &=\cos^4 A \\ \ &=\left(\cos^2 A\right)^2 \\ \ &=\left(\frac{1+\cos2 A}{2}\right)^2 \\  \ &=\frac{1}{4}\left(1+\cos2 A\right)^2 \\ \ &=\frac{1}{4}\left(1^2+2\times1\times\cos2 A+\cos^22 A\right) \\  \ &=\frac{1}{4}\left(1+2\cos2 A+\frac{1+\cos4 A}{2}\right) \\  \ &=\frac{1}{4}\left(\frac{2+4\cos2 A+1+\cos4 A}{2}\right) \\ \ &=\frac{3+4\cos2 A+\cos4 A}{8} \\ \ &= \frac{3}{8}+ \frac{4\cos 2A }{8} + \frac{\cos 4A}{8} \\ \ &= \frac{3}{8}+ \frac{1}{2}\cos 2A + \frac{1}{8}\cos 4A \\  \ &= \text{ RHS} \end{align}[/math][br][br]15. (c) Prove that: [math] \sin5\theta=16\sin^5\theta-20\sin^3\theta+5\sin \theta [/math][br]Solution:[br][math] \begin{align} \text{LHS } \ &=\sin5\theta \\ \ &=\sin\left(3\theta+2\theta\right) \\ \ &=\sin3\theta\cos2\theta+\cos3\theta\sin2\theta \\ \ &=\left(3\sin \theta-4\sin^3\theta\right)\cos2\theta+\left(4\cos^3\theta-3\cos \theta\right)\sin2\theta \\ \ &=3\sin \theta\cos2\theta-4\sin^3\theta\cos2\theta+4\cos^3\theta\sin2\theta-3\cos \theta\sin2\theta \\ \ &=3\sin \theta\left(1-2\sin^2\theta\right)-4\sin^3\theta\left(1-2\sin^2\theta\right) \\ \ &\ \ \ +4\cos^3\theta\left(2\sin \theta\cos \theta\right)-3\cos \theta\left(2\sin \theta\cos \theta\right) \\ \ &=3\sin \theta-6\sin^3\theta-4\sin^3\theta+8\sin^5\theta \\ \ &\ \ \ +8\sin \theta\cos^4\theta-6\sin \theta\cos^2\theta \\ \ &=3\sin \theta-10\sin^3\theta+8\sin^5\theta \\ \ &\ \ \ +8\sin \theta\left(\cos^2\theta\right)^2-6\sin \theta\left(1-\sin^2\theta\right) \\ \ &=3\sin \theta-10\sin^3\theta+8\sin^5\theta+8\sin \theta\left(1-\sin^2\theta\right)^2-6\sin \theta+6\sin^3\theta \\ \ &=8\sin^5\theta-4\sin^3\theta-3\sin \theta+8\sin \theta\left(1-2\sin^2\theta+\sin^4\theta\right) \\ \ &=8\sin^5\theta-4\sin^3\theta-3\sin \theta+8\sin \theta-16\sin^3\theta+8\sin^5\theta \\ \ &=16\sin^5\theta-20\sin^3\theta+5\sin \theta \\ \ &= \text{ RHS} \end{align} [/math][br][br]15 (d) Prove that: [math] \cos5A=16\cos^5A-20\cos^3A+5\cos A [/math][br]Solution:[br][math] \begin{align} \text{LHS } \ & =\cos5A \\ \ & =\cos\left(3A+2A\right) \\ \ & =\cos3A\cos2A-\sin3A\sin2A \\ \ & =\left(4\cos^3A-3\cos A\right)\cos2A \\ \ &\ \ \ \ -\left(3\sin A-4\sin^3A\right)\sin2A \\ \ & =4\cos^3A\cos2A-3\cos A\cos2A \\ \ & \ \ \ \ -3\text{sinA}\sin2A+4\sin^3A\sin2A \\ \ & =4\cos^3A\left(2\cos^2A-1\right)-3\cos A\left(2\cos^2A-1\right) \\ \ &\ \ \ \ -3\sin A\left(2\sin A\cos A\right)+4\sin^3A\left(2\sin A\cos A\right) \\ \ & =8\cos^5A-4\cos^3A-6\cos^3A+3\cos A \\ \ & \ \ \ \ -6\sin^2A\cos A+8\sin^4A\cos A \\ \ & =8\cos^5A-10\cos^3A+3\cos A \\ \ & \ \ \ \ -6\left(1-\cos^2A\right)\cos A+8\left(\sin^2A\right)^2\cos A \\ \ & =8\cos^5A-10\cos^3A+3\cos A \\ \ & \ \ \ \ -6\cos A+6\cos^3A+\cdot8\left(1-\cos^2A\right)^2\cos A \\ \ & =8\cos^5A-4\cos^3A-3\cos A \\ \ & \ \ \ \ +8\left(1-2\cos^2A+\cos^4A\right)\cos A \\ \ & =8\cos^5A-4\cos^3A-3\cos A \\ \ & \ \ \ \ +8\cos A-16\cos^3A+8\cos^5A \\ \ & =16\cos^5A-20\cos^3A+5\cos A \\ \ & = \text{ RHS} \end{align} [/math][br][br]16. With the help of multiple angles relation of Sine and Cosine, find the value of [math]\sin18^{\circ}, \sin36^{\circ} [/math] and [math] \sin54^{\circ}[/math]. By using these values, find the values of [math]\cos18^{\circ}, \cos36^{\circ} [/math] and [math]\cos54^{\circ}[/math]. Also, find the value of [math]\tan18^{\circ}, \tan36^{\circ}[/math] and [math]\tan54^{\circ}[/math] . Share your result to your friend and prepare combine report.[br][b]Solution:[/b][br][math] \begin{align} \text{ Let, } & \theta = 18^{\circ} \\ or, & \ 5\theta = 5\times 18^{\circ} \\ or, & \ 2\theta + 3\theta = 90^{\circ} \\ or, & \ 3\theta = 90^{\circ} - 2\theta \\ or, & \ \cos 3\theta = \cos (90^{\circ} - 2\theta )\\ or, & \ 4\cos^3\theta -3\cos \theta = \sin 2\theta \\ or, & \ \cos \theta [4\cos^2 \theta - 3 ] = 2\sin \theta \cos \theta \\ or, & \ 4(1-\sin^2 \theta ) -3 = 2\sin \theta \\ or, & \ 4 -4\sin^2 \theta -3 -2\sin \theta =0 \\ or, & \ -4\sin^2 \theta -2\sin \theta +1 = 0 \\ or, & \ -(4\sin^2 \theta +2\sin \theta -1) =0 \\ or, & \ 4\sin^2 \theta +2\sin \theta -1=0 \end{align} [/math] [br]Now, comparing with [math] ax^2+bx+c=0 [/math], we get[br] [math] a=4, b= 2, c= -1, x = \sin \theta [/math][br]Now,[br][math] \begin{align} \sin \theta & = \frac{-b\pm \sqrt{b^2 - 4ac}}{2a} \\ \ & =\frac{-2\pm \sqrt{(2)^2 -4 \times 4 \times (-1)}}{2\times 4 } \\ \ & = \frac{-2\pm \sqrt{4+16}}{8} \\ \ & = \frac{-2\pm\sqrt{20}}{8} \\ \ & = \frac{-2\pm 2\sqrt{5}}{8} \\ \ & = \frac{2(-1\pm \sqrt{5})}{8}\\ \ & =\frac{-1\pm\sqrt{5}}{4} \end{align} [/math][br]Since [math] \sin 18^{\circ} [/math] is positive,[br][math] \therefore \sin 18^{\circ} = \frac{-1+\sqrt{5}}{4}=\frac{\sqrt{5}-1}{4} [/math] [br]Now,[br][math] \begin{align} \cos 18^{\circ} &=\sqrt{1-\sin^2 18^{\circ}}\\ \ & = \sqrt{1-\left(\frac{\sqrt{5}-1}{4}\right)^2}\\ \ & = \sqrt{1-\frac{\left\{(\sqrt{5})^2-2\times \sqrt{5}\times 1+1^2 \right\}^2}{16}}\\ \ & = \sqrt{\frac{16-(5-2\sqrt{5}+1)}{16}}\\ \ & = \sqrt{\frac{16-5+2\sqrt{5}-1}{16}}\\ \ & = \sqrt{\frac{10+2\sqrt{5}}{16}}\\ \ & = \frac{\sqrt{10+2\sqrt{5}}}{4}\\ \therefore \cos 18^{\circ}& = \frac{\sqrt{10+2\sqrt{5}}}{4} \end{align} [/math][br]Now,[br][math] \begin{align} \tan 18^{\circ}& =\frac{\sin 18^{\circ}}{\cos 18^{\circ}}\\ \ & = \frac{\frac{\sqrt{5}-1}{4}}{\frac{\sqrt{10+2\sqrt{5}}}{4}}\\ \ & = \frac{\sqrt{5}-1}{\sqrt{10+2\sqrt{5}}}\\ \therefore \tan 18^{\circ}& = \frac{\sqrt{5}-1}{\sqrt{10+2\sqrt{5}}}\\ \end{align} [/math][br][br][math] \begin{align} \cos 36^{\circ}& = 1-2\sin^2 18^{\circ}\\ \ & = 1-2\left(\frac{\sqrt{5}-1}{4} \right)^2\\ \ & = 1 - 2\times \frac{(\sqrt{5})^2-2\times \sqrt{5}\times 1 +1^2 }{16}\\ \ & = 1 - \frac{5-2\sqrt{5}+1}{8} \\ \ & = \frac{8-5+2\sqrt{5}-1}{8} \\ \ & = \frac{2+2\sqrt{5}}{8} \\ \ & = \frac{2(1+\sqrt{5})}{8} \\ \text{or, } \cos 36^{\circ} &= \frac{1+\sqrt{5}}{4}\\ \therefore \cos 36^{\circ}& = \frac{\sqrt{5}+1}{4}\\ \end{align} [/math][br]Also,[br][math] \begin{align} \text{We know,}\\ \sin 36^{\circ}& = \sqrt{1-\cos^2 36^{\circ}}\\ \ & = \sqrt{1-\left( \frac{\sqrt{5}+1}{4} \right)^2}\\ \ & = \sqrt{1-\frac{(\sqrt{5})^2 +2\times \sqrt{5}\times 1+1^2 }{16}} \\ \ & = \sqrt{1-\frac{5 +2\times \sqrt{5}\times 1+1 }{16}} \\ \ & = \sqrt{1-\frac{6 + 2\sqrt{5} }{16}} \\ \ & = \sqrt{\frac{16-6 - 2\sqrt{5} }{16}} \\ \ & = \sqrt{\frac{10- 2\sqrt{5} }{16}} \\ \ & = \frac{\sqrt{10-2\sqrt{5}}}{4}\\ \therefore \sin 36^{\circ}\ & = \frac{\sqrt{10-2\sqrt{5}}}{4}\\ \end{align} [/math] [br]Also,[br][math] \begin{align} \tan 36^{\circ} & = \frac{\sin 36^{\circ} }{\cos 36^{\circ} }\\ \ & = \frac{ \frac{\sqrt{10-2\sqrt{5}}}{4}\\}{\frac{\sqrt{5}+1}{4}}\\ \ & =\frac{\sqrt{10-2\sqrt{5}}}{\sqrt{5}+1}\\ \therefore \tan 36^{\circ}& = \frac{\sqrt{10-2\sqrt{5}}}{\sqrt{5}+1}\\ \end{align} [/math][br]Also[br][math] \begin{align} \sin 54^{\circ} & = \sin(90^{\circ}-36^{\circ})\\ \ & =\cos 36^{\circ}\\ \ & = \frac{\sqrt{5}+1}{4}\\ \therefore \sin 54^{\circ}&=\frac{\sqrt{5}+1}{4}\\ \end{align} [/math] [br]Also,[br][math] \begin{align} \cos 54^{\circ} & = \cos(90^{\circ}-36^{\circ})\\ \ & =\sin 36^{\circ}\\ \ & = \frac{\sqrt{10-2\sqrt{5}}}{4}\\ \therefore \cos 54^{\circ}&=\frac{\sqrt{10-2\sqrt{5}}}{4}\\ \end{align} [/math] [br]Also,[br][math] \begin{align} \tan 54^{\circ} & = \frac{\sin 54^{\circ} } {\cos 54^{\circ} }\\ \ & =\frac{\frac{\sqrt{5}+1}{4} } { \frac{\sqrt{10-2\sqrt{5}}}{4}} \\ \ & =\frac{\sqrt{5}+1}{\sqrt{10-2\sqrt{5}}} \\ \therefore \ \tan54^{\circ} & =\frac{\sqrt{5}+1}{\sqrt{10-2\sqrt{5}}} \\ \end{align} [/math][br]
– AMBIK BARAL

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4.

Statistics

  • 1. Statistics-Class-10-Opt. Maths (2+4+4=10 Marks)

4.1.

Statistics-Class-10-Opt. Maths (2+4+4=10 Marks)

Introduction
[size=150][color=#0000ff][b]Quartile Deviation (Q.D.)[/b][/color][/size][br][list][*]The difference between the upper quartile and the lower quartile is called [color=#0000ff][b]INTERQUARTILE RANGE.[/b][/color][/*][*]The semi-interquartile range of the data is known as[b][color=#0000ff] Quartile Deviation(Q.D.)[/color][/b][/*][*]Here ,inter-quartile range [math]=Q_3-Q_1[/math] [/*][*]Semi- interquartile range [math]=\frac{Q_3-Q_1}{2}[/math] [/*][*]Coefficient of quartile deviation[math]=\frac{Q_3-Q_1}{Q_3+Q_1}[/math] [/*][/list][color=#0000ff]For continuous or grouped data[/color][br][list][*][math]\text{Position of }Q_1=\left(\frac{N}{4}\right)^{th}\text{ item}[/math] [/*][*][math] Q_1 =L+\frac{\frac{N}{4}-c.f.}{f} \times h [/math] [/*][*][math]\text{Position of }Q_3=\left(\frac{3N}{4}\right)^{th}\text{ item}[/math][/*][*][math]Q_3=L+\frac{\frac{3N}{4}-c.f.}{f}\times h[/math][br]Where,[br][math] L= [/math] lower limit of quartile class[br][math]c.f.= [/math] c.f. of the preceding class [br][math] f= [/math] frequency of quartile class[br][math]h=[/math] class -height or, class - size or class interval[/*][/list]
User Guideline
Dear learner,[br][list][*] Click [color=#00ff00][b]Green coloured[/b] [/color]buttons for table.[/*][*]Click[color=#00ff00] [/color][color=#00ffff][b]Cyan[/b] [/color][color=#333333]coloured buttons for solution steps.[/color][br][/*][*]To change data, click on [size=150][b] check box [/b]named[b] [/b][/size] [color=#ff0000]Ambik[/color] .[/*][*]Again click [b]check box[/b] .[/*][*]Again click [color=#00ff00][b]Green coloured[/b] [/color]buttons for table.[/*][*]Again click [color=#00ffff][b]Cyan[/b][/color] coloured buttons for solution steps.[/*][*]We can use this applet to check our answer steps and to teach our students.[/*][/list]
Find quartile deviation and its coefficient from the following data.
[list=1][*][math] \begin{tabular}{|c|c|c|c|c|c|c|} \hline C.I.& 0-10&10-20&20-30&30-40&40-50&50-60\\[br]\hline[br]f&7&10&8&6&6&2\\ [br]\hline[br]\end{tabular}[/math][color=#ff0000][ Ans: 12.17, 0.49][/color][br][br][/*][*][math]\begin{tabular}{|c|c|c|c|c|c|} \hline \text{Size of shoes} & 5-8&8-11&11-14&14-17&17-20\\[br]\hline[br] \text{No. of shoes} &7&10&8&6&4 \\ [br]\hline[br]\end{tabular} [/math][color=#ff0000][Ans: 3.06, 0.21 ][/color][br][br][/*][*][math] \begin{tabular}{|c|c|c|c|c|c|c|} \hline \text{Size of shoes} & 0-20&20-40&40-60&60-80&80-100&100-120\\[br]\hline[br] \text{No. of shoes} &3&8&10&12&10&8 \\ [br]\hline[br]\end{tabular}[/math][color=#ff0000][ Ans: 23.5, 0.35][/color][br][br][/*][*][math] \begin{tabular}{|c|c|c|c|c|c|c|} \hline \text{Wages (Rs. in thousand )} &6-8&8-10&10-12&12-14\\[br]\hline[br] \text{No. of workers} &85&65&60&50\\ [br]\hline[br]\end{tabular} [/math][[color=#ff0000]Ans: 1.99, 0.21][/color][br][br][/*][*][math] \begin{tabular}{|c|c|c|c|c|c|c|} \hline \text{Class Interval} &5-10&10-15&15-20&20-25&25-30 \\[br]\hline[br] \text{Frequency} &4&12&16&6&2\\ [br]\hline[br]\end{tabular}[/math][color=#ff0000][ Ans: 3.44, 0.22 ][/color][br][br][br][/*][/list]
Introduction
Mean Deviation[br]The average of the absolute values of the deviation of each item from mean, median or mode is known as a mean deviation. It is also known as average deviation. It is denoted by M.D.[br]Calculation of Mean Deviation[br]For continuous series[br][list=1][*]M.D. from mean [math] = \frac{\Sigma f|x-\overline{x}|} {N} [/math][/*][*]M.D. from median [math] = \frac{\Sigma f|x-m_d|}{N} [/math][/*][*]Coefficient of M.D. from mean [math] = \frac{M.D. }{Mean} [/math] [/*][*]Coefficient of M.D. from median [math] = \frac{M.D.}{Median} [/math][br]Where,[br][math]\text{Mean}\left(\overline{x}\right)=\frac{\Sigma fx}{N}[/math][br][math]\text{Median}\left(m_d\right)=L+\frac{\frac{N}{2}-c.f.}{f}\times h[/math][br][math] x =\text{ mid-value of class interval } [/math][br][/*][/list]
Standard Deviation
[size=150][b][color=#1e84cc][size=200]S[/size]tandard deviation[/color][/b] [/size]is the positive square root of the arithmetic mean of the square of deviations of given data taken from mean. It is also known as[color=#ff0000] [b]"Root mean square deviation"[/b][/color]. It is denoted by Greek letter [math]\sigma[/math] (read as sigma). It is considered as the best measure of dispersion because:[br][list=1][*]It's value is based on all the observations.[/*][*]Deviation of each term is taken from the central value.[/*][*]All algebraic sign are also considered[/*][/list][b][size=150][color=#ff0000]Calculation of Standard Deviation[/color][/size][/b][br][color=#0000ff]Actual mean method:[br][/color]Standard deviation(σ)[math]=\sqrt{\frac{\Sigma f\left(x-\overline{x}\right)^2}{N}}[/math], where [math]x[/math] is the mid-value of each class-interval.[br][color=#0000ff]Direct method:[/color][br]Standard deviation(σ)[math]=\sqrt{\frac{\Sigma fx^2}{N}-\left(\frac{\Sigma fx}{N}\right)^2}[/math] ,[math]x[/math] is the where is the mid-value of each class-interval.[br][color=#0000ff]Assumed mean method:[/color][br]Standard deviation(σ) [math]=\sqrt{\frac{\Sigma fd^2}{N}-\left(\frac{\Sigma fd}{N}\right)^2}[/math],[br] where, [math]d=x-A[/math][i],[br] [math]A=\text{Assumed mean }[/math][br][/i] [math]x=\text{\text{mid- value of class - interval.[br]}}[/math][br][color=#0000ff]Step deviation method:[br][/color]When the class-interval is very large then step deviation method is used to find the standard.[br]Standard deviation(σ) [math]=\sqrt{\frac{\Sigma fd'^2}{N}-\left(\frac{\Sigma fd'}{N}\right)^2}\times h[/math][br]Where[br][math]d'=\frac{x-A}{h},\text{ }x=\text{mid- value of class -interval}[/math][br][math]A=\text{Assumed mean}[/math][br][math]h=\text{class - size}[/math][br][color=#ff0000][b][size=200][size=150]Coefficient of variation (C.V.)[/size][/size][/b][/color][br] The relative measure of standard deviation is known as the coefficient of standard deviation and is defined by[br]Coefficient of standard deviation [math] = \frac{ \text{Standard Deviation} } {\text{mean} }=\frac{\sigma}{\overline{x}} [/math][br]If the coefficient of standard deviation is multiplied by 100, then it is known as coefficient of variation. Coefficient of variation is denoted by C.V. and is calculated as:[br]   [math] C.V. = \frac{\sigma}{\overline{x} } \times 100\% [/math][br]Greater the coefficient of variation, greater will be the variation and less will be the consistency or uniformity. Less the C.V., greater will be the consistency or uniformity. For the consistency or uniformity of distribution, we use the C.V. So, C.V. is used to compare given distributions.[br][br][color=#ff0000][b][size=150]Variance:[/size][/b][/color][br] The square of standard deviation(σ) is called variation. It is given by [br]       [math]\text{Varaince} = (\sigma)^2 [/math]
[list=1][*]Find the [color=#0000ff][b]standard deviation [/b][/color]of the following data[color=#ff0000].[SEE 2075 R', SEE 2073 S'][/color][color=#0000ff][b] [Ans: 11.49][/b][/color][color=#ff0000][br][/color][math] \begin{tabular}{|c|c|c|c|c|c|c|} \hline[br]\text{Class Interval}& 0-10& 10-20& 20-30& 30-40& 40-50\\[br]\hline[br]\text{Frequency}&5&8&15&16&6\\[br]\hline[br]\end{tabular}[br][/math][br][br][/*][*]Find the [b][color=#1e84cc]standard deviation[/color][/b] of the following data[color=#ff0000].[ 2070 S ][/color][color=#1e84cc][b] [Ans: 6.05 ][br][/b][/color][math]\begin{tabular}{|c|c|c|c|c|c|c|} \hline[br]\text{Marks}& 0-4&4-8&8-12&12-16&16-20&20-24\\[br]\hline[br]\text{No. of students}&7&7&10&15&7&6 \\[br]\hline[br]\end{tabular} [/math][/*][*]Find the [color=#1e84cc][b]standard deviation[/b][/color] and [color=#1e84cc][b]its coefficient[/b][/color] of the given data[color=#ff0000].[ 2069 R'] [/color][color=#0000ff][b][ Ans: 11.66, 0.35 ][br][/b][/color][math] \begin{tabular}{|c|c|c|c|c|c|c|} \hline[br]\text{Class - Interval}& 0-10&10-20&20-30&30-40&40-50\\[br]\hline[br]\text{No. of students}&5&15&25&35&45 \\[br]\hline[br]\end{tabular} [/math][br][br][/*][*]Calculate the [b][color=#1e84cc]coefficient of variation[/color][/b] from the data given below.[color=#ff0000][ 2075 R ] [/color][color=#1e84cc][b][ Ans: 44.1% ][br][/b][/color][math]\begin{tabular}{|c|c|c|c|c|c|c|} \hline[br]\text{Class - Interval}& 0-20&20-40&40-60&60-80&80-100\\[br]\hline[br]\text{No. of students}&2&3&4&5&6 \\[br]\hline[br]\end{tabular} [/math][br][br][/*][*]Find the[color=#1e84cc][b] standard deviation[/b][/color] and [b][color=#1e84cc]coefficient of variation[/color][/b] from the given data. [color=#ff0000][ SEE MODEL 2076 ] [/color][color=#0000ff][b][Ans: 6.05 & 50.42 % ][/b][/color][br][math] \begin{tabular}{|c|c|c|c|c|c|c|} \hline [br]\text {Age} & 0-4&4-8&8-12&12-16&16-20&20-24 \\ \hline[br]\text{ No. of students} & 7&7&10&15&7&6 \\ \hline[br]\end{tabular} [/math][/*][/list]
– AMBIK BARAL

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