Question

cos^2a - ctg^2a/ tg^2a - sin^2a

Answer 1

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

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

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

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