Cos (П/2-х) - sin3x+sin5x=0

Решим уравнение Cos (П/2 - х) - sin (3 * x) + sin (5 * x) = 0.

sin x - sin (3 * x) + sin (5 * x) = 0;

sin x - (sin (3 * x) - sin (5 * x)) = 0;

sin x - 2 * cos ((3 * x + 5 * x) / 2) * sin ((3 * x - 5 * x) / 2) = 0;

sin x - 2 * cos (8 * x/2) * sin (-2 * x/2) = 0;

sin x - 2 * cos (4 * x) * (-sin x) = 0;

sin x + sin x * 2 * cos (4 * x) = 0;

sin x * (1 + 2 * cos (4 * x)) = 0;

1) sin x = 0;

x = pi * n;

2) 2 * cos (4 * x) = - 1;

cos (4 * x) = - 1/2;

4 * x = + - arccos (-1/2) + 2 * pi * n;

4 * x = + - 2 * pi/3 + 2 * pi * n;

x = + - pi/6 + pi/2 * n.