Question

Найдите sin²a + 3 sin a * cos a + cos² a / 2 sin² a + 3 cos² a
Если tg a = 3

Answer 1

$tga=3\\frac{sin^2a+3sinacdot cosa+cos^2a}{2sin^2a+3cos^2a}=[; frac{:cos^2a}{:coss^2a}; ]= frac{tg^2a+3tga+1}{2tg^2a+3} = \\=frac{9+3cdot 3+1}{2cdot 9+3} = frac{19}{21}$