Вопрос пользователя:
cos^2 x – 1/2 sin 2x + cosx = sinx
Илюха отвечает:
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