Giải phương trình 2 cos ( x + pi/3 ) − 1 = 0 .

\(2\cos \left( {x + \frac{\pi }{3}} \right) - 1 = 0\)\( \Leftrightarrow 2\cos \left( {x + \frac{\pi }{3}} \right) - 1 = 0 \Leftrightarrow \cos \left( {x + \frac{\pi }{3}} \right) = \frac{1}{2}\)\( \Leftrightarrow \cos \left( {x + \frac{\pi }{3}} \right) = \cos \frac{\pi }{3}\)

\( \Leftrightarrow \left[ \begin{array}{l}x + \frac{\pi }{3} = \frac{\pi }{3} + k2\pi \\x + \frac{\pi }{3} = \frac{{ - \pi }}{3} + l2\pi \end{array} \right.\left( {k,l \in \mathbb{Z}} \right)\)\( \Leftrightarrow \left[ \begin{array}{l}x = k2\pi \\x = \frac{{ - 2\pi }}{3} + l2\pi \end{array} \right.\left( {k,l \in \mathbb{Z}} \right)\)