# How do you prove sin x + cot x cos x = csc x?

$\sin x + \left(\cos \frac{x}{\sin} x\right) . \cos x = \sin x + \frac{{\cos}^{2} x}{\sin x} =$
$= \frac{{\sin}^{2} x + {\cos}^{2} x}{\sin x} = \frac{1}{\sin x} = \csc x$