Question

Решите пожалуйста пример

Answer 1

$\frac{3\sin\alpha-5cos\alpha+2}{sin\alpha+3cos\alpha+6}=\frac{1}{3}$

$\frac{\frac{3\sin\alpha}{cos\alpha}-\frac{5cos\alpha}{cos\alpha}+\frac{2}{cos\alpha}}\frac{{sin\alpha}{cos\alpha}+\frac{3cos\alpha}{cos\alpha}+\frac{6}{cos\alpha}}=\frac{1}{3}$

$\frac{3tg\alpha-5+\frac{2}{cos\alpha}}{tg\alpha+3+\frac{6}{cos\alpha}}=\frac{1}{3}$

$9tg\alpha-15+\frac{6}{cos\alpha}=tg\alpha+3+\frac{6}{cos\alpha}}$

$9tg\alpha-tg\alpha=3+15$

$8tg\alpha=18\ /:8$

$tg\alpha=2 \frac{1}{4}$