We will take the left hand side and prove that it is equal to the right -hand side
But, First, we need to note that; cotx = cosx / sinx and csc²x = 1/ sin²x
substitute the values into the the left-hand side of the original equation
[tex]\frac{\frac{\cos x}{\sin x}}{\frac{1}{\sin ^2x}}[/tex][tex]\frac{\cos x}{\sin x}\times\frac{\sin ^2x}{1}[/tex]One of the sinx at the numerator will cancel-out the one at the denominator
[tex]=\text{ cosx sinx}[/tex]