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

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