Найдите значение выражения 24√6 cos π/4 · cos 11π/6.

\(\cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}\)
\(\cos \frac{11\pi}{6} = \cos (2\pi - \frac{\pi}{6}) = \cos (-\frac{\pi}{6}) = \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}\)
Подставляем:
\[24\sqrt{6} \cdot \cos \frac{\pi}{4} \cdot \cos \frac{11\pi}{6} = 24\sqrt{6} \cdot \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} = 24\sqrt{6} \cdot \frac{\sqrt{6}}{4} = 24 \cdot \frac{6}{4} = 6 \cdot 6 = 36\]