Prove that trigonometric equation isn't changed by value of x $\sqrt{\sin^4x+\cos2x} + \sqrt{\cos^4x-\cos2x}$ I have to prove that $x$ doesn't matter. However I can't get things to simplify.

Hint. One has
$$
\sin^4x+\cos2x=\sin^4x+2 \cos^2x-1=\sin^4x-2 \sin^2x+1
$$ and
$$
\cos^4x-\cos2x=\cos^4x-2 \cos^2x+1
$$ Can you finish it?
