Question

-ctg альфа - tg альфа делить на ctg альфа -tg альфа

Answer 1

$\frac{-Ctg\alpha-tg\alpha}{Ctg\alpha-tg\alpha}=-\frac{\frac{1}{tg\alpha}+tg\alpha}{\frac{1}{tg\alpha}-tg\alpha}=-\frac{\frac{1+tg^{2}\alpha}{tg\alpha}}{\frac{1-tg^{2}\alpha  }{tg\alpha}}=-\frac{(1+tg^{2}\alpha)*tg\alpha }{tg\alpha(1-tg^{2}\alpha)}=-\frac{1+tg^{2}\alpha}{1-tg^{2}\alpha}=-\frac{1}{Cos2\alpha}\\\\Otvet:\boxed{-\frac{1}{Cos2\alpha}}$