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

[latex](sin\frac{7\pi}{8}-cos\frac{7\pi}{8})^2=sin^2\frac{7\pi}{8}-2sin\frac{7\pi}{8}cos\frac{7\pi}{8}+cos^2\frac{7\pi}{8}=\\(sin^2\frac{7\pi}{8}+cos^2\frac{7\pi}{8})-sin(2*\frac{7\pi}{8})=-sin\frac{7\pi}{4}=-sin(2\pi-\frac{\pi}{4})=\\=sin\frac{\pi}{4}=\frac{\sqrt2}{2}[/latex]