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