sin^4 x=1-cos^4 x. sin^4 x=1-cos^4 x

sin^4(x) + cos^4(x) = 1
(sin^2(x) +cos^2(x))^2 -2sin^2(x)*cos^2(x) = 1
4sin^2(x)*cos^2(x) = 0
sin^2(2x) = 0
cos(4x) = 1

4x = 2pi*n
x=pi/2 n
n - целое число