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

[latex] \frac{sin^2 \alpha -tg^2 \alpha }{cos^2 \alpha -ctg^2 \alpha }= \frac{sin^2 \alpha - \frac{sin^2 \alpha }{cos^2 \alpha } }{cos^2 \alpha - \frac{cos^3 \alpha }{sin^2 \alpha } } = \\ = \frac{sin^2 \alpha *cos^2 \alpha -sin^2 \alpha }{cos^2 \alpha }* \frac{sin^2 \alpha }{sin^2 \alpha *cos^2 \alpha -cos^2 \alpha }= \\ = \frac{sin^2 \alpha *sin^2 \alpha(cos^ 2\alpha -1)}{cos^2 \alpha *cos^ \alpha (sin^2 \alpha -1)}= \\ = \frac{-sin^6 \alpha }{-cos^6 \alpha }=tg^6 \alpha [/latex]