Question

Решите уравнение 3sin квадрат x - 4 sin x cos x + 5 cos квадрат x =2

Answer 1

$3sin^2x-4sinxcosx+5cos^2x=2(sin^2x+cos^2x) \\ sin^2x-4sinxcosx+3cos^2x=0 | :cos^2x \\ tg^2x-4tgx+3=0 \\ tgx = 1 \\ tgx =3 \\ x= \frac{ \pi }{4} + \pi n \\ x=arctg3 + \pi n$