Tính \(M = \cos a + \cos \left( {a + {{120}^0}} \right) + \cos \left( {a - {{120}^0}} \right)\)

* Hướng dẫn giải

\(\begin{array}{l}
M = \cos a + \cos \left( {a + {{120}^0}} \right) + \cos \left( {a - {{120}^0}} \right)\\
 = \cos a + \cos a.\cos {120^0} - \sin a.\sin {120^0} + \cos a.\cos {120^0} + \sin a.\sin {120^0}\\
 = \cos a + \cos a.\left( { - \frac{1}{2}} \right) - \sin a.\frac{{\sqrt 3 }}{2} + \cos a.\left( { - \frac{1}{2}} \right) + \sin a.\frac{{\sqrt 3 }}{2}\\
 = 0
\end{array}\)