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Math Help - one more identity proof

  1. #1
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    one more identity proof

    Prove the identity:

    tan(x/2) + cot(x/2) = 2 csc(x)
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  2. #2
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    Quote Originally Posted by Mr_Green View Post
    Prove the identity:

    tan(x/2) + cot(x/2) = 2 csc(x)
    \frac{\sin \frac{x}{2}}{\cos \frac{x}{2}} + \frac{\cos \frac{x}{2}}{\sin \frac{x}{2}} = \frac{\sin^2 \frac{x}{2} + \cos^2 \frac{x}{2}}{\sin \frac{x}{2} \cos \frac{x}{2}} = \frac{1}{\sin \frac{x}{2} \cos \frac{x}{2}} = \frac{2}{2\sin \frac{x}{2}\cos \frac{x}{2}} = \frac{2}{\sin x} = 2\csc x
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