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