Cotangent of a Sum: Discovery

[color=#000000]The applet below contains a rectangle with[/color][color=#980000] [/color][color=#bf9000][b]2 similar triangles[/b].[/color][color=#980000] [/color][b]The upper right segment has length 1.  [/b][color=#000000]There are 7 expressions shown off to the right.  [br][br][/color][b]Your job is to [/b][b]carefully drag each expression (label) next to the segment (in the figure) whose length is given by this expression. [/b] [i][color=#000000]Don't bother labeling the dashed hypotenuse of the right triangle in the middle.  Leave this dashed segment blank (without a label.)[b]  [/b][/color][/i]
[size=100][size=150]Study the following diagram carefully. [br][br]Can you write an expression for [math]cot\left(\alpha+\beta\right)[/math]? [/size][/size]
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Information: Cotangent of a Sum: Discovery