Question

Доказать тригонометрическое тождество:
$cos alpha = frac{1-tg^{2} frac{alpha}{2} }{1+tg^{2} frac{alpha}{2} }$

Answer 1

$frac{1-tg^2 frac{alpha}{2} }{1+tg^2 frac{alpha}{2} } = frac{1- frac{sin^2 frac{alpha}{2} }{cos^2 frac{alpha}{2} } }{1+ frac{sin^2 frac{alpha}{2} }{cos^2 frac{alpha}{2} } } = frac{cos^2 frac{alpha}{2} -sin^2 frac{alpha}{2} }{cos^2 frac{alpha}{2} +sin^2 frac{alpha}{2} }= frac{cos(2* frac{alpha}{2} )}{1}=cos alpha$

Answer 2

Огромное спасибо!