cos^2x = 1/2(1-cosx)
cos^2x = 1/2 - 1/2cosx
2cos^2x = 1 - cosx
2cos^2x + cosx - 1 = 0
Замена: t = cos(x)
2t^2 + t - 1 = 0
D = 1 + 8 = 9
t1 = (-1 + 3)/4 = 1/2t2 = (-1 - 3)/4 = -1
cos(x) = 1/2 или cos(x) = -1
x = π/3 + 2πn, 2π/3 + 2πn, а также x = π + 2πn.
cos^2x = 1/2(1-cosx)
cos^2x = 1/2 - 1/2cosx
2cos^2x = 1 - cosx
2cos^2x + cosx - 1 = 0
Замена: t = cos(x)
2t^2 + t - 1 = 0
D = 1 + 8 = 9
t1 = (-1 + 3)/4 = 1/2
t2 = (-1 - 3)/4 = -1
cos(x) = 1/2 или cos(x) = -1
x = π/3 + 2πn, 2π/3 + 2πn, а также x = π + 2πn.