cos 2x = 1 - 2sin^2 x4sin^4 x = (2sin^2 x)^2 = (1 - cos 2x)^2 = 1 - 2cos 2x + cos^2 2xsin^2 2x = 1 - cos^2 2xПодставляем1 - 2cos 2x + cos^2 2x + 1 - cos^2 2x = 12 - 2cos 2x = 1cos 2x = -1/22x = ± 2pi/3 + 2pi*nx = ± pi/3 + pi*n
cos 2x = 1 - 2sin^2 x
4sin^4 x = (2sin^2 x)^2 = (1 - cos 2x)^2 = 1 - 2cos 2x + cos^2 2x
sin^2 2x = 1 - cos^2 2x
Подставляем
1 - 2cos 2x + cos^2 2x + 1 - cos^2 2x = 1
2 - 2cos 2x = 1
cos 2x = -1/2
2x = ± 2pi/3 + 2pi*n
x = ± pi/3 + pi*n