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