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

[latex]tg2\alpha=\frac{2tg\alpha}{1-tg^2\alpha}\\\frac{tg\frac{\pi}{8}}{1-tg^2\frac{\pi}{8}}=\frac{2tg\frac{\pi}{8}}{2(1-tg^2\frac{\pi}{8})}=\frac{1}{2}*(\frac{2tg\frac{\pi}{8}}{1-tg^2\frac{\pi}{8}})=\frac{1}{2}*tg(2*\frac{\pi}{8})=\frac{1}{2}*tg\frac{\pi}{4}=\\=\frac{1}{2}*1=\frac{1}{2}[/latex]