Вычислите (cos π/8-sin π/8)(cos π/8+sin π/8).

\[\left( \cos\frac{\pi}{8} - \sin\frac{\pi}{8} \right)\left( \cos\frac{\pi}{8} + \sin\frac{\pi}{8} \right) =\]

\[= \cos^{2}\frac{\pi}{8} - \sin^{2}\frac{\pi}{8} =\]

\[= \cos\left( 2 \cdot \frac{\pi}{8} \right) = \cos\frac{\pi}{4} = \frac{\sqrt{2}}{2}\ \]