1) cosx=cos3x 2sinx*cosx=cosx

Найдем корни уравнения.

1) cos x = cos (3 * x);

cos x - cos (3 * x) = 0;

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

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

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

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

sin x * sin (2 * x) = 0;

{ sin x = 0;

sin (2 * x) = 0;

{ x = пи * n, n ∈ Z;

2 * x = пи * n, n ∈ Z;

{ x = пи * n, n ∈ Z;

x = пи/2 * n, n ∈ Z.

2) sin x * cos x = cos x;

sin x * cos x - cos x = 0;

sin x * (1 * cos x - 1) = 0;

sin x * (cos x - 1) = 0;

{ sin x = 0;

cos x - 1 = 0;

{ sin x = 0;

cos x = 1;

{ x = пи * n, n ∈ Z;

x = 2 * пи * n, n ∈ Z.