Question

Вычислить:
$frac{5sin alpha +7cos alpha }{6cos alpha -3sin alpha } , tg alpha = frac{4}{15}$

Answer 1

$tga=frac{sina}{cosa}=frac{4}{15}\ sina=frac{4cosa}{15}\ \ frac{5sina+7cosa}{6cosa-3sina}=frac{frac{4cosa}{3}+7cosa}{6cosa-frac{4cosa}{5}}=\ frac{frac{25cosa}{3}}{frac{26cosa}{5}}=frac{125}{78}$