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