Докажите тождество cos^2x - sin^2x/(ctg^2x - tg^2x) = sin^2x * cos^2x

Question

Докажите тождество cos^2x - sin^2x/(ctg^2x - tg^2x) = sin^2x * cos^2x

Answer 1

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