2010-10-02, 07:43 PM
Wait, what? No you can't. You can use difference of squares, though.
cos^4 - sin^4 = (cos^2)^2 - (sin^2)^2 = (cos^2 + sin^2)(cos^2 - sin^2) = 1(cos^2 - sin^2) = cos 2x.
arccos cos 2x = 2x.
cos^4 - sin^4 = (cos^2)^2 - (sin^2)^2 = (cos^2 + sin^2)(cos^2 - sin^2) = 1(cos^2 - sin^2) = cos 2x.
arccos cos 2x = 2x.

