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