так и раскрывать
sin^2 2x = (sin 2x)^2 = (2sin x*cos x)^2 = 4sin^2 x*cos^2 x
cos^2 2x = (cos 2x)^2 = (cos^2 x - sin^2 x)^2 = cos^4 x - 2sin^2 x*cos^2 x + sin^4 x
cos^2 2x + (sin^2 2x) / 2 = cos^4 x - 2sin^2 x*cos^2 x + sin^4 x + 2sin^2 x*cos^2 x = sin^4 x + cos^4 x
