Sinx-sin2x+sin5x+sin8x=0

Решите уравнение.

Sin5x+sinx+sin8x - sin2x = 0;

2sin3xcos2x + 2sin3xcos5x=0;

2sin3x (cos5x + cos2x) = 0;

sin3xcos7x/2*cos3x/2 = 0;

sin3x=0 ⇒3x = π*k ⇔x = π/3*k, k∈Z.

cos7x/2=0⇒7x/2 = π/2+π*k ⇔x = π/7+2π/7*k, k∈Z.

cos3x/2 = 0 ⇒3x/2 = π/2+π*k ⇔x = π/3+2π/3*k, k∈Z.