Question

verify the identity cot x/ csc^2 x= cos x sin x

Answer 1

$\frac{\cot x}{\csc ^2x}=\text{ cosx sinx}$

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

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

$\frac{\cos x}{\sin x}\times\frac{\sin ^2x}{1}$

One of the sinx at the numerator will cancel-out the one at the denominator

$=\text{ cosx sinx}$