Đáp án:
\[H = 0\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
H = \cos \dfrac{{2\pi }}{9} + \cos \dfrac{{4\pi }}{9} + \cos \dfrac{{8\pi }}{9}\\
= \cos \dfrac{{2\pi }}{9} + \left( {\cos \dfrac{{8\pi }}{9} + \cos \dfrac{{4\pi }}{9}} \right)\\
= \cos \dfrac{{2\pi }}{9} + 2.\cos \dfrac{{\dfrac{{8\pi }}{9} + \dfrac{{4\pi }}{9}}}{2}.\cos \dfrac{{\dfrac{{8\pi }}{9} - \dfrac{{4\pi }}{9}}}{2}\\
= \cos \dfrac{{2\pi }}{9} + 2\cos \dfrac{{2\pi }}{3}.\cos \dfrac{{2\pi }}{9}\\
= \cos \dfrac{{2\pi }}{9} + 2.\left( { - \dfrac{1}{2}} \right).\cos \dfrac{{2\pi }}{9}\\
= \cos \dfrac{{2\pi }}{9} - \cos \dfrac{{2\pi }}{9}\\
= 0
\end{array}\)
