Cos^2 x - 1/2 sin 2x + cosx = sinx

cos² x - 0,5 sin 2x + cosx = sinx cos² x -  sin x·cosx + cosx - sinx = 0 (cos² x + cosx) -  (sin x·cosx + sinx) = 0 cosx·(cos x + 1 ) - sin x·(cosx + 1) = 0 (cos x + 1)·(cosx - sin x) = 0 1) cos x + 1 = 0 cos x = -1 х₁ = π + 2πn 2) cosx - sin x = 0 делим на cosx 1 - tgх = 0 tgх = 1 х₂ = π/4 + πn Ответ: х₁ = π + 2πn, х₂ = π/4 + πn