Решите уравнение

2 sinx+sin 2x=cosx+1

2sinx + sin2x = cosx = 1

2sinx + sin2x - cosx - 1 = 0

sinx (2 + sinx - cosx - 1) = 0

1) sinx = 0

x = πn, n ∈ Z

2) sinx - cosx + 1 = 0 / : cosx

tgx + 1 = 0

tgx = - 1

x = π/4 + 2πn, n ∈ Z

Ответ: 1) x = πn, n ∈ Z,

2) x = π/4 + 2πn, n ∈ Z