Giải phương trình sau: sin x - sin 2x + sin 3x = 0

\(\sin x - \sin 2x + \sin 3x = 0 \Leftrightarrow \left( {\sin x + \sin 3x} \right) - \sin 2x = 0\)

\( \Leftrightarrow 2\sin 2x\cos x - \sin 2x = 0\)\( \Leftrightarrow \)\(\sin 2x\left( {2\cos x - 1} \right) = 0 \Leftrightarrow \left[ \begin{array}{l}\sin 2x = 0\\\cos x = \frac{1}{2}\end{array} \right.\)                                                     \( \Leftrightarrow \left[ \begin{array}{l}2x = k\pi \\x =  \pm \frac{\pi }{3} + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = k\frac{\pi }{2}\\x =  \pm \frac{\pi }{3} + k\pi \end{array} \right.\)