Answer
Showed that given statement, $\frac{\cot\theta}{\csc\theta}$ = $\cos\theta$,
is an identity as left side transforms into right side.
Work Step by Step
Given statement is-
$\frac{\cot\theta}{\csc\theta}$ = $\cos\theta$
Left Side = $\frac{\cot\theta}{\csc\theta}$
= $\frac{\cos\theta/\sin\theta}{1/\sin\theta}$
(Using reciprocal identity)
= $ \frac{\cos\theta}{\sin\theta} \times \frac{\sin\theta}{1}$
= $\cos\theta$
= Right Side
i.e. Left Side transforms into Right Side
i.e. Given statement, $\frac{\cot\theta}{\csc\theta}$ = $\cos\theta$,
is an identity.
