cos^2 x-3sinx*cosx=-1

cos^2 x - 3 * sin x * cos x = - 1;

Упростим уравнение.

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

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

Приведем подобные.

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

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

Разделим уравнение на cos^2 x.

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

tg^2 x - 3 * tg x + 2;

a^2 - 3 * a + 2 = 0;

D = 9 - 4 * 1 * 2 = 1;

x1 = (3 + 1) / 2 = 4/2 = 2;

a2 = (3 - 1) / 2 = 2/2 = 1;

1) tg x = 2;

x = arctg 2 + пи * n;

2) tg x = 1;

x = пи/4 + пи * n.