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