Решите уравнение sin9x-sin7x+sin3x-sinx=0

(Sin9x - Sinx) + (Sin3x - Sin7x) = 0

2Sin4x Cos5x - 2Sin2xCos5x = 0

Cos5x (Cos4x - Sin2x) = 0

Cos5x = 0 или Cos4x - Sin2x = 0

5x = π/2 + πк, к ∈Z 1 - 2Sin²2x - Sin2x = 0

x = π/10 + πk / 5, к ∈Z 2Sin²2x + Sin2x - 1 = 0

а) Sinx = (-1 + 3) / 4 = 1/2

х = (-1) ^nπ/3 + nπ, n ∈Z

б) Sinx = - 1

x = - π/2 + πm, m ∈Z