sinx*sin3x+sin4x*sin8x=0

1/2 * (cos (x - 3x) - cos (x + 3x) + cos (4 x - 8x) - cos (4x + 8x)) = 1/2 (cos 2x - cos 4x + cos 4x - cos 12x) = 1/2 (cos 2x - cos 12x) = 1/2 * ( - 2) sin 7x * sin 5x = 0;

Следовательно:

sin 7x = 0 = > 7x = πn = > x = πn/7;

sin 5x = 0 = > 5x = πn = > x = πn/5.