Question

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

Answer 1

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