Question

Prove the identity with steps.

Answer 1

Remember that a double angle formula for cosine is

`\cos(2x)=\cos^(2)x-\sin^(2)x`

So

`\cos^(2)(2x)-\sin^(2)(2x)=\cos(4x)`

`\rightarrow \cos^(2)(2x)-\sin^(2)(2x)=\cos(2*2x)`

`\rightarrow \cos^(2)(2x)-\sin^(2)(2x)=\cos^(2)(2x)-\sin^(2)(2x)`