√8(cos(5π/8)·cos(π/8) − sin(5π/8)·sin(π/8)) =

По формуле косинуса суммы: \(\cos x\cos y-\sin x\sin y=\cos(x+y)\).

\(\sqrt{8}\cos\left(\frac{5\pi}{8}+\frac{\pi}{8}\right)=\sqrt{8}\cos\frac{3\pi}{4}=2\sqrt{2}\cdot\left(-\frac{\sqrt{2}}{2}\right)=-2.\)

Ответ: −2.