Question

Вычислить, если $tg alpha$ = 2
$frac{2 + sin alpha cos alpha }{1 + 5cos^{2} alpha }$

Answer 1

$frac{2+sin alpha cos alpha }{1+5cos^2 alpha } =$
$= frac{frac{2}{cos^2 alpha }+frac{sin alpha cos alpha }{cos^2 alpha }}{frac{1}{cos^2 alpha }+frac{5cos^2 alpha}{cos^2 alpha } }=frac{(frac{2}{cos^2 alpha }-2)+2+tg alpha }{(frac{1}{cos^2 alpha }-1)+1+5 }=frac{2tg^2 alpha +2+tg alpha }{tg^2 alpha +6 }=2+frac{tg alpha -10}{tg^2 alpha +6 }=$
$2+frac{2 -10}{4 +6 }=2-0,8=1,2$