Question

Помогите с вычислением выражения

Answer 1

$cos^2x=frac{1+cos2x}{2}\\(cosfrac{7pi}{8})^2=(cos(pi-frac{pi}{8}))^2=(-cosfrac{pi}{8})^2=cos^2frac{pi}{8}=frac{1+cos(2*frac{pi}{8})}{2}=\=frac{1}{2}+frac{cosfrac{pi}{4}}{2}=frac{1}{2}+frac{sqrt{2}}{4}\\...=sqrt{2}-sqrt{8}(frac{1}{2}+frac{sqrt{2}}{4})=[sqrt{8}=sqrt{4*2}=2sqrt{2}]=\=sqrt{2}-2sqrt{2}(frac{1}{2}+frac{sqrt{2}}{4})=sqrt{2}-sqrt{2}-frac{2sqrt{2}*sqrt{2}}{4}=-frac{4}{4}=-1$



$sin2x=2sinx*cosx\\2sin(frac{5pi}{6})cos(frac{5pi}{6})=sin(2*frac{5pi}{6})=sinfrac{5pi}{3}=sin(2pi-frac{pi}{3})=\=-sinfrac{pi}{3}=-frac{sqrt{3}}{2}$