Question

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

Answer 1

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