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

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