Cos^2a - ctg^2a/ tg^2a - sin^2a - Все ответы

Решите задачу:

$\frac{cos^{2} \alpha -ctg ^{2} \alpha }{tg ^{2} \alpha -sin ^{2} \alpha } =(cos ^{2} \alpha - \frac{cos ^{2} \alpha }{sin ^{2} \alpha } ):( \frac{sin ^{2} \alpha }{cos ^{2} \alpha }-sin ^{2} \alpha )=$

$=( \frac{cos ^{2} \alpha *sinx^{2} \alpha -cosx^{2} \alpha }{sin ^{2} \alpha } ):( \frac{sin ^{2} \alpha -cos ^{2} \alpha *sin ^{2} \alpha }{cos ^{2} \alpha } )=$

$= \frac{cos ^{2} \alpha *(sin ^{2} \alpha -1 ) }{sin ^{2} \alpha } : \frac{sin ^{2} \alpha *(1-cos ^{2} \alpha ) }{cos ^{2} \alpha } =$

$= \frac{cos ^{2} \alpha *(-cos ^{2} \alpha )*cos ^{2} \alpha }{sin ^{2} \alpha *sin ^{2} \alpha *sin \alpha ^{2} } =- \frac{cos ^{6} \alpha }{sin ^{6} \alpha } =-ctg ^{6} \alpha$