решите уравнение cos2x+cos4x+2sin^2x/2=1
Cos 2x + cos 4x + 2sin² x/2 = 1 cos 2x + cos 4x = 1 - 2sin² x/2 cos 2x + cos 4x = cos x 2 cos( (4x-2x) / 2) cos ( (4x+2x) / 2) = cos x 2 cos x cos 3x = cos x 2 cos 3x = 1 cos 3x = 1/2 3x = ±arccos 1/2 + 2πk 3x = ±π/6 + 2πk x = ±π/18 + 2πk/3, k∈Z.)