Question

Решите уравнение
2 sinx+sin 2x=cosx+1

Answer 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