Cos x-cos 3x + sin x=0

cos x - cos 3x + sin x = 0;

2sin 2x sin x + sin x = 0;

sin x (2sin 2x + 1) = 0;

sin x = 0;

x = пn, n∈Z;

2sin 2x + 1 = 0;

sin 2x = - 1/2;

2x = + arcsin (-1/2);

2x = 2 пk - arcsin (-1/2);

2x = 2 пk - п/6; k∈Z;

2x = 2 пk + 7 п/6; k∈Z;

x1 = пk - п/12; k∈Z;

x2 = пk + 7 п/12; k∈Z;

Ответ: x = пn, n∈Z; x1 = пk - п/12; k∈Z; x2 = пk + 7 п/12; k∈Z;