А) Решите уравнение:

2sin (п+x) = sin2x-3sin^3 x

2sin (п+x) = sin2x-3sin^3 x

-2Sinx = Sin2x-3Sin^3 x

-2Sinx - 2SinxCosx + 3Sin^3 x = 0

Sinx (-2 - 2Cosx + 3Sin² x) = 0

Sinx = 0 или 3Sin²x - 2Cosx - 2 = 0

x = πn, n ∈ Z 3 (1 - Cos²x) - 2Cosx - 2 = 0

3 - 3Cos²x - 2Cosx - 2 = 0

3Cos²x + 2Cosx - 1 = 0

Cosx = (-1 + - √4) / 3 = (-1 + - 2) / 3

Cosx = - 1, Cosx = 1/3

х = π + 2πk, k ∈Z x = + - arcCos (1/3) + 2πm,

m∈Z