Question

Решите тригонометрическое уравнение:

3sin(x)^2-7sin(x)*cos(x)+2cos(x)^2=0

Даю 50 баллов

Answer 1

$\displaystyle 3sin^2x-7sinx*cosx+2cos^2x=0\bigg|:cos^2x\neq 0\\\\3tg^2x-7tgx+2=0\\\\tgx=t\\\\3t^2-7t+2=0\\\\D=49-24=25\\\\t_{1.2}=\frac{7 \pm 5}{6} \\\\t_1=2; t_2=\frac{1}{3}\\\\tgx=2; x=arctg2+\pi n; n \in Z\\\\tgx=\frac{1}{3}; x=arctg\frac{1}{3}+\pi n; n \in Z$