Question

$frac{2}{3+4Cos2a}$ , , если tga=1/5

Answer 1

$frac{2}{3+4cos 2 alpha }= frac{2sin^2 alpha +2cos^2 alpha }{3sin^2 alpha +3cos^2 alpha +4cos^2 alpha -4sin^2 alpha } =\ \ \ = frac{2sin^2 alpha +cos^2 alpha }{-sin^2 alpha +7cos^2 alpha } = frac{2tg^2 alpha +1}{-tg^2 alpha +7} = frac{2* frac{1}{25} +1}{- frac{1}{25}+7 } = frac{2+25}{-1+25*7} = frac{27}{174}$