# How do you verify the identity: cos^2x−sin^2x = 1−2sin^2x

We have to prove the identity $\cos ^{2}x -\sin ^{2}x = 1-2\sin ^{2}x$

### Proof

We know the trigonometric identity

$\cos ^{2}x +\sin ^{2}x = 1$

We can rewrite it as

$\cos ^{2}x =1-\sin ^{2}x$

Now for the given equation

$\cos ^{2}x -\sin ^{2}x$

= $(1 -\sin ^{2}x)- \sin ^{2}x$ {from (i)}

=$1 -2 \sin ^{2}x$

= RHS

Hence Proved