Решить уравнение sin7x+cos4x=sinx

sin7x - sinx + cos4x = 0;

2sin3x · cos4x + cos4x = 0;

cos4x (2sin3x + 1) = 0;

1) cos4x = 0;

4x = π/2 + πn;

x = π/8 + πn/4, n∈Z;

2) 2sin3x + 1 = 0;

sin3x = - 1/2;

3x = (-1) ^ (k) · π/6 + πk;

x = (-1) ^ (k) · π/18 + πk/3, k∈Z;

Ответ:x = π/8 + πn/4, n∈Z; x = (-1) ^ (k) · π/18 + πk/3, k∈Z;