(5cos2a+3)/(3-8cos^2 a) , если tg a= минус корень из 5

[latex] frac{5cos2 alpha +3}{3-8cos^2 alpha } = frac{5cos^2 alpha -5sin^2 alpha +3sin^2 alpha +3cos^2 alpha }{3sin^2 alpha +3cos^2 alpha -8cos^2 alpha } = frac{8cos^2 alpha -2sin^2 alpha }{3sin^2 alpha -5cos^2 alpha } =\ = frac{8tg^2 alpha -2}{3-5tg^2 alpha } = frac{8cdot(- sqrt{5})^2-2 }{3-5cdot(-sqrt{5})^2} = frac{8cdot5-2}{3-5cdot5}= frac{40-2}{3-25}= frac{38}{-22}= - frac{19}{11}=-1 frac{8}{11} [/latex]