Докажите тождество[latex] \frac{tg ^{2} \alpha -sin ^{2} \alpha }{ctg ^{2} \alpha -cos ^{2} \alpha } =tg ^{2} \alpha [/latex]

[latex] \frac{tg^2 \alpha -sin^2 \alpha }{ctg^2 \alpha -cos^2a} =tg^6 \alpha \\ \\ \frac{ \frac{sin^2 \alpha }{cos^2 \alpha } -sin^2 \alpha }{ \frac{cos^2 \alpha }{sin^2 \alpha } -cos^2a} =tg^6 \alpha \\ \\ \frac{ \frac{sin^2 \alpha -sin^2 \alpha *cos^2 \alpha }{cos^2 \alpha } }{ \frac{cos^2 \alpha -cos^2 \alpha *sin^2 \alpha }{sin^2 \alpha } } =tg^6 \alpha \\ \\ \frac{(sin^2 \alpha -sin^2 \alpha *cos^2 \alpha)*sin^2 \alpha }{(cos^2 \alpha -cos^2 \alpha *sin^2 \alpha)*cos^2 \alpha } =tg^6 \alpha [/latex] [latex] \frac{sin^2 \alpha (1-cos^2 \alpha )sin^2 \alpha }{cos^2 \alpha(1- sin^2 \alpha )cos^2 \alpha } =tg^6 \alpha \\ \\ \frac{sin^2 \alpha*sin^2 \alpha*sin^2 \alpha}{cos^2 \alpha*cos^2 \alpha*cos^2 \alpha} =tg^6 \alpha \\ \\ \frac{sin^6 \alpha }{cos^6 \alpha } =tg^6 \alpha \\ \\ tg^6 \alpha =tg^6 \alpha [/latex]