Решите уравнение cos x-cos 3x+sin x=0

cos(x) - cos(3x) + sin(x) = 0

cos(x) - 4cos³(x) + 3cos(x) + sin(x) = 0

4cos(x)*(1 - cos²(x)) + sin(x) = 0

4cos(x)*sin²(x) + sin(x) = 0

sin(x)*(4cos(x)*sin(x) + 1) = 0

sin(x)*(2sin(2x) + 1) = 0

sin(x) = 0 --> x = πk.

sin(2x) = -1/2 --> x = -π/12 + πk; x = -5π/12 + πk.

Ответ: {πk; -π/12 + πk; -5π/12 + πk\ k ∈ Z}.