Question

tgП/8/1-tg^2П/8 помогите срочно!!!!!!!!

Answer 1

$tg frac{ pi }{8} -tg^2 frac{ pi }{8} = frac{sin frac{ pi }{8} }{cosfrac{pi}{8}}-frac{sin^2 frac{ pi }{8} }{cos^2frac{pi}{8}}=frac{sin frac{ pi }{8}bullet cosfrac{ pi }{8} -sin^2frac{pi}{8}}{cos^2frac{pi}{8}}=\\=frac{frac{1}{2}(sin0+sin frac{ pi }{4})-sin^2frac{pi}{8} }{cos^2frac{pi}{8}}=frac{frac{1}{2}sinfrac{pi}{4}-frac{1-cosfrac{pi}{4}}{2}}{frac{1+cosfrac{pi}{4}}{2}}=\\\=frac{sinfrac{pi}{4}-1+cosfrac{pi}{4}}{1+cosfrac{pi}{4}}$

$frac{ frac{ sqrt{2}}{2}-1+frac{sqrt{2}}{2}}{1+frac{sqrt{2}}{2}}=frac{sqrt{2}-1}{frac{2+sqrt{2}}{2}}=frac{2sqrt{2}-2}{sqrt{2}+2}.$