1) Cosx - cos3x = 3sin^2x 2) 3tg^2x - 8cos^2x +

Вычислим корешки уравнений.

1) Cos x cos (3 * x)  = 3 * sin^2 x;

Упростим уравнение. 

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

-2 * sin (-2 * x/2) * sin (4 * x/2) = 3 * sin^2 x;

-2 * sin (-x) * sin (2 * x) = 3 * sin^2 x;

2 * sin x * sin (2 * x) = 3 * sin^2 x;

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

3 * sin^2 x 2 * sin x * 2 * sin x * cos x = 0;

Применим свойства степеней.

3 * sin^2 x 4 * sin^2 x * cos x = 0; 

sin^2 x * (3 4 * cos x) = 0;

sin^2 x = 0;

3 4 * cos x = 0;

sin x = 0;

4 * cos x = 3;

x = пи * n, n Z;

x = +-arccos (3/4) + 2 * пи * n, n Z.

 2) 3 * tg^2 x  - 8 * cos^2 x  + 1 = 0;

3 * sin^2 x/cos^2 x 8 * cos^2 x + 1 = 0;

3 * sin^2 x 5 * cos^4 x + cos^2 x = 0;

3  * (1 cos^2 x) 5 * cos^4 x + cos^2 x = 0; 

-5 * cos^4 x + cos^2 x 3 * cos^2 x + 3 = 0;

5 * cos^4 x + 2 * cos^2 x 3 = 0;

D = 4 4 * 5 * (-3) = 4 + 20 * 3 = 64 = 8^2;

cos^2 x = (-2 + 8)/(2 * 5) = 6/10 = 3/5;

cos^2 x = (-2 8)/10 = -10/10 = -1;

1) cos^2 x = -1;

Нет корней.

2) cos^2 x = 0.6;

cos x = +-0.6;

cos x = +0.6;

cos x = -0.6;

x = +-arccos (0.6) + 2 * пи * n, n Z;

x = +-arccos (-0.6) + 2 * пи * n, n Z.