Question

(tg pi/8)/1-tg^2pi/8 помогите с тригонометрией

Answer 1

$tg2alpha=frac{2tgalpha}{1-tg^2alpha}\frac{tgfrac{pi}{8}}{1-tg^2frac{pi}{8}}=frac{2tgfrac{pi}{8}}{2(1-tg^2frac{pi}{8})}=frac{1}{2}*(frac{2tgfrac{pi}{8}}{1-tg^2frac{pi}{8}})=frac{1}{2}*tg(2*frac{pi}{8})=frac{1}{2}*tgfrac{pi}{4}=\=frac{1}{2}*1=frac{1}{2}$