[size=150][b]Recall the angle addition/subtraction and double angle identities. Give all common variations.[br][br][/b]Whilst you are learning the identities, write the full equation for the identity.[/size][br][br][i][color=#5b0f00][b]Example:[/b][/color][br][br][/i][b]Question:[/b][br] Reciprocal identity:[br] [math]\sin\left(x\right)=[/math][br][br][b]Answer:[/b][br] [math]\sin\left(x\right)=\frac{1}{\csc\left(x\right)}[/math]
Angle addition identity for sine[br][math]\sin\left(x+y\right)=[/math]
[math]\sin\left(x+y\right)=\sin\left(x\right)\cos\left(y\right)+\sin\left(y\right)\cos\left(x\right)[/math]
Double angle identity for tangent[br][math]\tan\left(2x\right)=[/math]
[math]\tan\left(2x\right)=\frac{2\tan\left(x\right)}{1-\tan^2x}[/math]
Angle addition identity for cosine[br][math]\cos\left(x+y\right)=[/math]
[math]\cos\left(x+y\right)=\cos\left(x\right)\cos\left(y\right)-\sin\left(x\right)\sin\left(y\right)[/math]
Angle subtraction identity for tangent[br][math]\tan\left(x-y\right)=[/math]
[math]\tan\left(x-y\right)=\frac{\tan\left(x\right)-\tan\left(y\right)}{1+\tan\left(x\right)\tan\left(y\right)}[/math]
Double angle identity for sine[br][math]\sin\left(2x\right)=[/math]
[math]\sin\left(2x\right)=2\sin\left(x\right)cos\left(x\right)[/math]
Angle addition identity for tangent[br][math]\tan\left(x+y\right)=[/math]
[math]\tan\left(x+y\right)=\frac{\tan\left(x\right)+\tan\left(y\right)}{1-\tan\left(x\right)\tan\left(y\right)}[/math]
Angle subtraction identity for cosine[br][math]\cos\left(x-y\right)=[/math]
[math]\cos\left(x-y\right)=\cos\left(x\right)\cos\left(y\right)+\sin\left(x\right)\sin\left(y\right)[/math]
Angle subtraction identity for sine[br][math]\sin\left(x-y\right)=[/math]
[math]\sin\left(x+y\right)=\sin\left(x\right)\cos\left(y\right)-\sin\left(y\right)\cos\left(x\right)[/math]
Double angle identity for cosine[br][math]\cos\left(2x\right)=[/math]
[math]\cos\left(2x\right)=\cos^2\left(x\right)-\sin^2\left(x\right)[/math][br][br][math]\cos\left(2x\right)=2\cos^2\left(x\right)-1[/math][br][br][math]\cos\left(2x\right)1-2\sin^2\left(x\right)[/math]