Giá trị đúng của \(\cos \frac{{2\pi }}{7} + \cos \frac{{4\pi }}{7} + \cos \frac{{6\pi }}{7}\) bằng :

* Hướng dẫn giải

Ta có \(\cos \frac{{2\pi }}{7} + \cos \frac{{4\pi }}{7} + \cos \frac{{6\pi }}{7} = \frac{{\sin \frac{\pi }{7}\left( {\cos \frac{{2\pi }}{7} + \cos \frac{{4\pi }}{7} + \cos \frac{{6\pi }}{7}} \right)}}{{\sin \frac{\pi }{7}}}\)

\( = \frac{{\sin \frac{{3\pi }}{7} + \sin \left( { - \frac{\pi }{7}} \right) + \sin \frac{{5\pi }}{7} + \sin \left( { - \frac{{3\pi }}{7}} \right) + \sin \pi  + \sin \left( { - \frac{{5\pi }}{7}} \right)}}{{2\sin \frac{\pi }{7}}} = \frac{{\sin \left( { - \frac{\pi }{7}} \right)}}{{2\sin \frac{\pi }{7}}} =  - \frac{1}{2}\)