How to prove this trigonometric expression? How would you go about proving the following?
$${1- \cos A \over \sin A } + { \sin A \over 1- \cos A} = 2 \operatorname{cosec} A $$
This is what I've done so far:
$$LHS = {1+\cos^2 A -2\cos A + 1 - \cos^2A \over \sin A(1-\cos A)}$$
....no idea how to proceed .... X_X

Hint:
$1-\cos A=1-(1-2 \sin^2\dfrac{A}{2})=2\sin^2 \dfrac{A}{2}$
$\dfrac{2 \sin^2 \dfrac{A}{2}}{2 \sin \dfrac{A}{2} \cos \dfrac{A}{2}}=\tan \dfrac{A}{2}$
The other expression will be $\cot \dfrac{A}{2}$
$(\tan^2 \dfrac{A}{2}+1) /\tan\dfrac{A}{2}= \dfrac{\sec^2 A \cos \dfrac{A}{2}}{\sin \dfrac{A}{2}}= \dfrac{1}{2 \sin A}$
