Proving A Trigonometric Identity- Double Angles $(\cos(2x)-\sin(2x))(\sin(2x)+\cos(2x)) = \cos(4x)$ I'm trying to prove that the left side equals the right side. I'm just stuck on which double angle formula of cosine to use.

$$(\cos(2x)-\sin(2x))(\sin(2x)+\cos(2x))=(\cos^2(2x)-\sin^2(2x)) = \cos(4x)$$
From
$$\cos(a+b)=\cos a \cos b-\sin a\sin b$$ if $a=2x,b=2x$ then
$$\cos(4x)=\cos^22x-\sin^22x$$
