Biểu thức 2cos pi/7 . cos 2pi/7 + cos 4pi/7 + cos 6pi/7 bằng

* Hướng dẫn giải

$$\begin{gathered} 2\cos \frac{\mathrm{\pi }}{7}.\cos \frac{2\mathrm{\pi }}{7}+\cos \frac{4\mathrm{\pi }}{7}+\cos \frac{6\mathrm{\pi }}{7} \\ =2\cos \frac{\mathrm{\pi }}{7}.\cos \frac{2\mathrm{\pi }}{7}+2\cos \frac{5\mathrm{\pi }}{7}\cos \frac{\mathrm{\pi }}{7} \\ =2\cos \frac{\mathrm{\pi }}{7}\left(\cos \frac{2\mathrm{\pi }}{7}+\cos \frac{5\mathrm{\pi }}{7}\right) \\ =4\cos \frac{\mathrm{\pi }}{7}\cos \frac{\mathrm{\pi }}{2}\cos \frac{3\mathrm{\pi }}{14} \\ =4\cos \frac{\mathrm{\pi }}{7}.0.\cos \frac{3\mathrm{\pi }}{14}=0 \end{gathered}$$