Question

1/1-tga-1/1+tga при a = pi/8
Помогли пожалуйста

Answer 1

$\frac{1}{1-tg\alpha}-\frac{1}{1+tg\alpha}=\frac{1+tg\alpha-1+tg\alpha}{(1-tg\alpha)(1+tg\alpha)}=\frac{2tg\alpha}{1-tg^{2}\alpha}= tg2\alpha\\\\\alpha=\frac{\pi}{8}\Rightarrow tg2\alpha=tg(2*\frac{\pi}{8})=tg\frac{\pi}{4}=1$