Question

Вычислите значение выражения 9cos^2a если ctga=√(4/11)

Answer 1

$Ctg\alpha=\sqrt{\frac{4}{11}} \\\\1+Ctg^{2}\alpha=\frac{1}{Sin^{2}\alpha}\\\\Sin^{2}\alpha=\frac{1}{1+Ctg^{2}\alpha}=\frac{1}{1+(\sqrt{\frac{4}{11}})^{2}}=\frac{1}{1+\frac{4}{11}}=\frac{1}{\frac{15}{11}}=\frac{11}{15}\\\\9Cos2\alpha=9(1-2Sin^{2}\alpha)=9*(1-2*\frac{11}{15})=9*(1-\frac{22}{15})=9*(-\frac{7}{15})=-\frac{21}{5}=-4,2\\\\Otvet:\boxed{9Cos2\alpha=-4,2}$