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