Cos^2x+tg^2x+sin^2x=1/sin^2x доказать тождество

Question

Cos^2x+tg^2x+sin^2x=1/sin^2x доказать тождество

Answer 1

(cos^2x - sin^2x)/(ctg^2x - tg^2x)=cos2x/(cos^4x-sin^4x)/(sinxcosx)^2=cos2x/(cos2x)/(sinxcosx)^2=sin^2xcos^2x