Question

Помогите решить пример если ctg=4

Answer 1

$frac{2Sin^{2} alpha-Cos^{2}alpha}{Sin^{2}alpha+3Cos^{2} alpha} =frac{frac{2Sin^{2}alpha}{Sin^{2}alpha}-frac{Cos^{2}alpha}{Sin^{2}alpha}}{frac{Sin^{2}alpha}{Sin^{2}alpha}+frac{3Cos^{2}alpha}{Sin^{2}alpha }}=frac{2-Ctg^{2}alpha}{1+3Ctg^{2}alpha}=frac{2-(frac{1}{4})^{2}}{1+3*(frac{1}{4})^{2}}=frac{2-frac{1}{16} }{1+frac{3}{16} }=frac{31}{16}:frac{19}{16}=frac{31*16}{16*19}=frac{31}{19}=1frac{12}{19}$