Verify that $\cos 2 x = 2 \cos 2 x - 1$

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Solution

$C os 2 x = \cos^{2} x - \sin^{2} x$ ………(1)
we have learnt that
$\cos^{2} x + \sin^{2} x = 1$
So, $\sin^{2} x = 1 - \cos^{2} x$
Substituting in equation (1) we get
$C o s 2 x = \cos^{2} x - (1 - \cos^{2} x)$
$C o s 2 x = 2 \cos^{2} x - 1$

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