Question

Доказать тождество
Cos2a= 1-tg^2a/1+tg^2a

Answer 1

$frac{1-tg^2a}{1+tg^2a}= frac{1- frac{sin^2a}{cos^2a} }{1+ frac{sin^2a}{cos^2a} }= frac{ frac{cos^2a-sin^2a}{cos^2a} }{ frac{cos^2a+sin^2a}{cos^2a} } = \ \ = frac{cos^2a-sin^2a}{cos^2a}* frac{cos^2a}{1}=cos^2a-sin^2a=cos2a$