Question

Вычислите (решение полностью)
корень из 2 /2 -(cos П/8 + sin П/8)^2=

Answer 1

$\sqrt{2}/2-(cos \pi /8+sin \pi /8)^2=\\= \sqrt{2}/2-(cos^2 \pi /8+2sin \pi /8*cos \pi/8+sin^2 \pi /8)=\\= \sqrt{2}/2-(1+sin(2* \pi /8))= \sqrt{2}/2-(1+sin \pi /4)=\\= \sqrt{2}/2-(1+ \sqrt{2}/2)= \sqrt{2}/2-1- \sqrt{2}/2=1$