Question

(Sin 7pi/8 - cos 7pi/8)^2

Answer 1

$(sinfrac{7pi}{8}-cosfrac{7pi}{8})^2=sin^2frac{7pi}{8}-2sinfrac{7pi}{8}cosfrac{7pi}{8}+cos^2frac{7pi}{8}=\(sin^2frac{7pi}{8}+cos^2frac{7pi}{8})-sin(2*frac{7pi}{8})=-sinfrac{7pi}{4}=-sin(2pi-frac{pi}{4})=\=sinfrac{pi}{4}=frac{sqrt2}{2}$