Tích số \(\cos \frac{\pi }{7}.\cos \frac{{4\pi }}{7}.\cos \frac{{5\pi }}{7}\) bằng :

* Hướng dẫn giải

\(\begin{array}{l}
\cos \frac{\pi }{7}.\cos \frac{{4\pi }}{7}.\cos \frac{{5\pi }}{7} = \frac{{\sin \frac{{2\pi }}{7}.\cos \frac{{4\pi }}{7}.\cos \frac{{5\pi }}{7}}}{{2\sin \frac{\pi }{7}}} =  - \frac{{\sin \frac{{2\pi }}{7}.\cos \frac{{2\pi }}{7}.\cos \frac{{4\pi }}{7}}}{{2\sin \frac{\pi }{7}}} =  - \frac{{\sin \frac{{4\pi }}{7}.\cos \frac{{4\pi }}{7}}}{{4\sin \frac{\pi }{7}}}\\
 =  - \frac{{\sin \frac{{8\pi }}{7}}}{{8\sin \frac{\pi }{7}}} = \frac{1}{8}
\end{array}\)