Giải phương trình: sin ( x − pi/3 ) = cos ( pi/ 2 − x ) .

\[\begin{array}{l}\sin \left( {x - \frac{\pi }{3}} \right) = \cos \left( {\frac{\pi }{2} - x} \right) \Leftrightarrow \sin \left( {x - \frac{\pi }{3}} \right) = \sin x \Leftrightarrow \left[ \begin{array}{l}x - \frac{\pi }{3} = x + k2\pi \\x - \frac{\pi }{3} = \pi  - x + k2\pi \end{array} \right.\\ \Leftrightarrow 2x = \frac{{4\pi }}{3} + k2\pi \, \Leftrightarrow x = \frac{{2\pi }}{3} + k\pi \,{\rm{ }}\left( {k \in \mathbb{Z}} \right).\end{array}\]