Упростите выражение:  [latex] \frac{sin ^{2} \alpha -tg ^{2} \alpha }{cos^{2} \alpha -ctg ^{2} \alpha } [/latex]

sin²a -tg²a=sin²a - sin²a/cos²a=(sin²acos²a - sin²a)/cos²a=sin²a(cos²a-1)/cos²a= =-sin^4a/cos²a cos²a - ctg²a=cos²a - cos²a/sin²a=(cos²asin²a - cos²a)/sin²a=cos²a(sin²a-1)/sin²a= =-cos^4a/sin²a (sin²a -tg²a)/(cos²a - ctg²a)=-sin^4a/cos²a : -cos^4a/sin²a=sin^4a/cos²a * sin²a/cos^4a= =sin^6a/cos^6a=tg^6a