Доказать тождество: (sin^2t+cos^2t/tg^2t*/1-cos^2t)=1

(1/(sin^2t/cos^2t)*cos^2t) - cos^2t/(1-cos^2t)=1
(1/sin^2t) - (cos^2t/sin^2t)=1
(1-cos^2t)/sin^2t=1
sin^2t/sin^2t=1
1=1
ч.т.д.