Question

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

Answer 1

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