sin3x sin6x-sin5x sin8x=0

sin7x+sin6x=sinx

Применяем формулы

sinα + sin β = 2sin ((α + β) / 2) ·cos ((α - β) / 2)

sin (α) = 2sin ((α) / 2) ·cos ((α) / 2)

2sin ((7x+6x) / 2) ·cos ((7x-6x) / 2) = 2sin (x/2) ·cos (x/2)

2cos (x/2) · (sin (13x/2) - sin (x/2)) = 0

2cos (x/2) ·2sin ((13x/2) - (x/2)) / 2 · cos ((13x/2) + (x/2)) / 2 = 0

4cos (x/2) · sin (3x) ·cos (7x/2) = 0

cos (x/2) = 0 или sin3x=0 или cos (7x/2) = 0

(x/2) = (π/2) + πk или 3 х=πn или (7 х/2) = (π/2) + πm,

k, n, m ∈ Z

x=π+2πk или х = (π/3) n или х = (π/7) + (2π/7) m,

k, n, m ∈ Z

x=π+2πk можно получить из (π/7) + (2π/7) m, при m=3: 10: 17, ..., (3+7p)

О т в е т. (π/3) n; (π/7) + (2π/7) m,

n, m ∈ Z