Answer
As left side transforms into right side, hence given identity-
$\frac{\cot A}{\csc A}$ = $\cos A$ is true.
Work Step by Step
Given identity is-
$\frac{\cot A}{\csc A}$ = $\cos A$
Taking L.S.
$\frac{\cot A}{\csc A}$
= $\frac{\cos A/\sin A}{1/\sin A}$
( Using reciprocal and ratio identities)
= $\frac{\cos A}{\sin A} . \frac{\sin A}{1}$
= $\cos A$ = R.S.
As left side transforms into right side, hence given identity-
$\frac{\cot A}{\csc A}$ = $\cos A$ is true.
