Question

Ну помогиииитеее
1-tg^2 π/8

Answer 1

$1-tg^2a=1- frac{sin^2a}{cos^2a}= frac{cos^2a-sin^2a}{cos^2a} = frac{cos2a}{frac{1+cos2a}{2}} = frac{2cos2a}{1+cos2a} \\Forvylu:; ; cos^2a-sin^2a=cos2a,; ; cos^2a=frac{1+cos2a}{2}\\1-tg^2frac{pi}{8}=frac{2cosfrac{pi}{4}}{1+cosfrac{pi}{4}}= frac{2cdot frac{sqrt2}{2}}{1+frac{sqrt2}{2}} =frac{2sqrt2}{2+sqrt2}= frac{2sqrt2(2-sqrt2)}{4-2} =sqrt2(2-sqrt2)$