one more identity proof

Quote:

Originally Posted by Mr_Green

Prove the identity:

tan(x/2) + cot(x/2) = 2 csc(x)

$\frac{\sin \frac{x}{2}}{\cos \frac{x}{2}} + \frac{\cos \frac{x}{2}}{\sin \frac{x}{2}} = \frac{\sin^2 \frac{x}{2} + \cos^2 \frac{x}{2}}{\sin \frac{x}{2} \cos \frac{x}{2}} = \frac{1}{\sin \frac{x}{2} \cos \frac{x}{2}} = \frac{2}{2\sin \frac{x}{2}\cos \frac{x}{2}} = \frac{2}{\sin x} = 2\csc x$