Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\sin x - \sin 2x + \sin 3x\\
= \left( {\sin 3x + \sin x} \right) - \sin 2x\\
= 2.\sin \dfrac{{3x + x}}{2}.\cos \dfrac{{3x - x}}{2} - 2\sin x.\cos x\\
= 2.\sin 2x.\cos x - 2\sin x.\cos x\\
= 2\cos x.\left( {\sin 2x - \sin x} \right)\\
= 2.\cos x.2.\cos \dfrac{{2x + x}}{2}.sin\dfrac{{2x - x}}{2}\\
= 4\cos x.\cos \dfrac{{3x}}{2}.\sin \dfrac{x}{2}
\end{array}\)