Answer
As left side transforms into right side, hence given identity-
$\tan \theta - \cot\theta$ = $\frac{\sin^{2}\theta - \cos^{2}\theta}{\sin\theta \cos\theta}$ is true.
Work Step by Step
Given identity is-
$\tan \theta - \cot\theta$ = $\frac{\sin^{2}\theta - \cos^{2}\theta}{\sin\theta \cos\theta}$
Taking L.S.
$\tan \theta - \cot\theta$
= $\frac{\sin\theta}{\cos \theta} - \frac{\cos\theta}{\sin\theta}$
( Using ratio identities)
= $\frac{\sin\theta}{\cos \theta}. \frac{\sin\theta}{\sin \theta} - \frac{\cos\theta}{\sin\theta}. \frac{\cos\theta}{\cos \theta}$
=$\frac{\sin^{2} \theta - \cos^{2} \theta}{\sin\theta \cos\theta}$
= R.S.
As left side transforms into right side, hence given identity-
$\tan \theta - \cot\theta$ = $\frac{\sin^{2}\theta - \cos^{2}\theta}{\sin\theta \cos\theta}$ is true.
