Question

cos^2 - sin^2 / ctg^2 - tg^2 = sin^2 * cos^2

помогите доказать тождество

Answer 1

ctg^2a-tg^2a=cos^2a/sin^2a-sin^2a/cos^2a=(cos^4a-sin^4a)/cos^2a*sin^2a=cos2a/(sinacosa)^2

 

(cos^2a-sin^2a)/(cos2a)/(sinacosa)^2=sin^2a*cos^2a