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