Answer
As left side transforms into right side, hence given identity-
$\csc^{2} \theta - \cot^{2} \theta$ = $1$ is true.
Work Step by Step
Given identity is-
$\csc^{2} \theta - \cot^{2} \theta$ = $1$
Taking L.S.
$\csc^{2} \theta - \cot^{2} \theta$
= $\frac{1}{\sin^{2} \theta} - \frac{\cos^{2} \theta}{\sin^{2} \theta}$
= $\frac{1 - \cos^{2} \theta}{\sin^{2} \theta}$
= $\frac{\sin^{2} \theta}{\sin^{2} \theta}$
( Using first Pythagorean identity, $1 -\cos^{2} \theta = \sin^{2} \theta$)
= $1$
= R.S.
As left side transforms into right side, hence given identity-
$\csc^{2} \theta - \cot^{2} \theta$ = $1$ is true.
