Question

156 номер решите .....

Answer 1

$(1+tg^2frac{pi}{8})(1+tg^2frac{3pi}{8})=frac{1}{cos^2frac{pi}{8}}cdot frac{1}{cos^2frac{3pi}{8}}=frac{1}{(cosfrac{pi}{8}cdot cosfrac{3pi}{8})^2}=\\=frac{1}{(frac{1}{2}cdot (cosfrac{2pi}{8}+cosfrac{4pi}{8}))^2}=frac{4}{(cosfrac{pi}{4}+cosfrac{pi}{2})^2}=frac{4}{(frac{sqrt2}{2}+0)^2}=frac{4}{frac{2}{4}}=8$