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