2sinx + 3cosx + 3 = 0 решите уравнение

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

2 * √ (1 - cos^2 x) + 3 * cos x + 3 = 0;

2 * √ (1 - cos^2 x) = - 3 * cos x - 3;

2 * √ (1 - cos^2 x) = (-3 * cos x - 3);

Dозведем уравнение в квадрат.

(2 * √ (1 - cos^2 x)) ^2 = (-3 * cos x - 3) ^2;

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

4 - 4 * cos^2 x = 9 * (cos x + 1) ^2;

4 - 4 * cos^2 x = 9 * (cos^2 x + 2 * cos x + 1);

4 - 4 * cos^2 x = 9 * cos^2 x + 18 * cos x + 9;

13 * cos^2 x + 18 * cos x + 5 = 0;

1) cos x = - 1;

x = pi + 2 * pi * n.

2) cos x = - 5/13;

x = + -arccos (-5/13) + 2 * pi * n.