# How do you solve Cos x / (1- sin x) = sec x + tan x?

$\frac{\cos x}{1 - \sin x} \cdot \frac{\cos x}{\cos} x$
$= \frac{{\cos}^{2} x}{\left(1 - \sin x\right) \cos x}$
$= \frac{{\sin}^{2} x - 1}{\left(1 - \sin x\right) \cos x}$
$= \frac{\left(1 + \sin x\right) \cancel{\left(1 - \sin x\right)}}{\cancel{\left(1 - \sin x\right)} \cos x}$
$= \frac{1}{\cos} x + \frac{\sin x}{\cos} x$
$= \sec x + \tan x$