Question

Алгебра.Доказать тождество

Answer 1

$sfdisplaystyle frac{1-cos2alpha+sin2alpha}{1+cos2alpha+sin2alpha}=tgalpha\\ frac{1-(1-2sin^2alpha)+2cosalphasinalpha}{1+2cos^2alpha-1+2cosalphasinalpha}=frac{sinalpha}{cosalpha}\\ frac{2sin^2alpha+2cosalphasinalpha}{2cos^2alpha+2cosalphasinalpha}=frac{sinalpha}{cosalpha}\\ frac{sinalpha(2sinalpha+2cosalpha)}{cosalpha(2sinalpha+2cosalpha)}=frac{sinalpha}{cosalpha}\\ frac{sinalpha}{cosalpha}=frac{sinalpha}{cosalpha}$

Ч.Т.Д.