Question

Найти тангенс альфа,если :

Answer 1

$frac{7sin alpha +13cos alpha }{5sin alpha -17cos alpha } =frac{3}{1}\\frac{7sin alpha +13cos alpha }{5sin alpha -17cos}=[frac{:cos alpha }{:cos alpha }]=frac{7cdot frac{sin alpha }{cos alpha }+13}{5cdot frac{sin alpha }{cos alpha }-17}=frac{7cdot tg alpha +13}{5cdot tg alpha -17}=frac{3}{1}\\7tg alpha +13=3(5tg alpha -17)\\7tg alpha +13=15tg alpha -51\\8tg alpha =64\\tg alpha =8\\oo$