Кандрюкова Татьяна
Ve
Vesta
sin^2 x - 3 cos^2 x - 4 sin x = 0
sin^2 x + cos^2 x - 4 cos^2 x - 4 sin x = 0
1 - 4 (cos^2 x + sin x) = 0
cos^2 x + sin x = 1/4
1 - sin^2 x + sin x = 1/4
- (sin^2 x - sin x) + 1 - 1/4 = 0
sin^2 x - sin x - 3/4 = 0
sin x = t, t [-1; 1]
t^2 - t - 3/4 = 0
D = 1 + 4 * 3/4 = 1 + 3 = 4
t 1 +/- 2 ) / 2
t1 = 1.5 не принадлежит [-1; 1]
t2 = -0.5
sin x = - 0.5
Ответ:
х = 7/6 П + 2 Пn
и
11/6 П + 2 Пn