Giải phương trình: cos 2x + pi/3 = sin x

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

\( \Leftrightarrow \left[ \begin{array}{l}2x + \frac{\pi }{3} = \frac{\pi }{2} - x + k2\pi \\2x + \frac{\pi }{3} = - \left( {\frac{\pi }{2} - x} \right) + k2\pi \end{array} \right.\)\( \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{{18}} + k\frac{{2\pi }}{3}\\x = - \frac{{5\pi }}{6} + k2\pi \end{array} \right.;k \in \mathbb{Z}\)