Question

Тригонометрия 

$frac{sin^{2} alpha - tg^{2} alpha } {cos^{2} alpha -ctg^{2} alpha }$

Answer 1

$frac{sin^2 alpha -tg^2 alpha }{cos^2 alpha -ctg^2 alpha }= frac{sin^2 alpha - frac{sin^2 alpha }{cos^2 alpha } }{cos^2 alpha - frac{cos^3 alpha }{sin^2 alpha } } = \ = frac{sin^2 alpha *cos^2 alpha -sin^2 alpha }{cos^2 alpha }* frac{sin^2 alpha }{sin^2 alpha *cos^2 alpha -cos^2 alpha }= \ = frac{sin^2 alpha *sin^2 alpha(cos^ 2alpha -1)}{cos^2 alpha *cos^ alpha (sin^2 alpha -1)}= \ = frac{-sin^6 alpha }{-cos^6 alpha }=tg^6 alpha$