Question

Помогите решить пример если ctg=4

Answer 1

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