# How do you verify (1 - cos x) / (1 + cos x) = (csc x - cot x)^2?

Verify $\frac{1 - \cos x}{1 + \cos x} = {\left(\csc x - \cot x\right)}^{2}$
$\left(\frac{1 - \cos x}{1 + \cos x}\right) \left(\frac{1 - \cos x}{1 - \cos x}\right) =$
$= {\left(1 - \cos x\right)}^{2} / \left(1 - {\cos}^{2} x\right) = {\left(1 - \cos x\right)}^{2} / \left({\sin}^{2} x\right) =$
$= {\left(\frac{1 - \cos x}{\sin x}\right)}^{2} = {\left(\frac{1}{\sin x} - \left(\cos \frac{x}{\sin} x\right)\right)}^{2} =$
$= {\left(\csc x - \cot x\right)}^{2}$