помогите решить sin^4 (x) + cos^4 (x) = cos^2 (2x) + 1/4

sin 4x = 2 sin 3x cos x - sin 2x

sin 4x = (sin x) (2 (-1 + 4cos2x) (cos x) - (2 cos x))

sin 4x = (sin x) ((-2 cos x + 8cos3x) - (2 cos x))

sin 4x = (sin x) (-4 cos x + 8cos3x)

cos 4x = 2 cos 3x cos x - cos 2x

cos 4x = 2 (-3cos x + 4cos3x) cos x - (-1 + 2cos2x)

cos 4x = (-6cos2x + 8cos4x) - (-1 + 2cos2x)

cos 4x = 1 - 8cos2 x + 8cos4x

cos^4x=cos^2x*cos^2x

sin^4 x=sin^2 x*sin^2 x

cos^2x = (1+cos2x) / 2