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