Question

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

Answer 1

`(\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

`((\cos x)/(\sin x))/((1)/(\sin ^2x))`

`(\cos x)/(\sin x)*(\sin ^2x)/(1)`

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

`=\text{ cosx sinx}`