I need help with this problem. I have to prove that cos^2(2x)-cos^2x = sin^2x-sin^2(2x)
That is equivalent to requiring that
cos^2x + sin^2x = cos^2(2x) + sin^2(2x)
That is always true, since both sides equal 1.
I realize you are not supposed to provide identities that way, but I see no problem with that shortcut.