Question

Cos^2(2x)-sin^2(2x)=0

Answer 1

\[\cos^2(2x)-\sin^2(2x)=0?\]

Answer 2

is it an identity?

Answer 3

This is an identity:
\[\large\rm \cos^2(\color{orangered}{x})-\sin^2(\color{orangered}{x})=\cos(2\color{orangered}{x})\]Hopefully you can see how this might be useful,\[\large\rm \cos^2(\color{orangered}{2x})-\sin^2(\color{orangered}{2x})=\cos(2\cdot\color{orangered}{2x})\]
It allows you to rewrite the left side of your equation as cos(4x).

Answer 4

but where does the cos in the rhs come from?

Answer 5

@zepdrix