# How do you prove the identity 1 / (1- cosx) + 1/ (1+ cosx) = 2 csc^2x?

Apr 15, 2015

Working with the left hand side

$\frac{\left(1 + \cos x\right) + \left(1 - \cos x\right)}{\left(1 - \cos x\right) \left(1 + \cos x\right)}$

$\frac{1 + \cos x + 1 - \cos x}{1 - {\cos}^{2} x}$

$\frac{2}{\sin} ^ 2 x$

$2 {\csc}^{2} x$

which is equal to the right hand side