# How do you prove Sinx = 1/sinx - cosx/tanx?

$\frac{1}{\sin x} - \cos \frac{x}{\sin \frac{x}{\cos} x} = \frac{1 - {\cos}^{2} x}{\sin x} =$
$= {\sin}^{2} \frac{x}{\sin x} = \sin x$