Giải phương trình sinx + sin2x + sin3x= cosx + cos2x + cos3x.

sinx + sin2x + sin3x= cosx + cos2x+ cos3x

⇔ 2sin2xcosx + sin2x = 2cos2xcosx + cos2x

⇔ sin2x(2cosx + 1) = cos2x(2cosx + 1)

⇔ (2cosx + 1)(sin2x – cos2x) = 0

⇔ \(\left[ \begin{array}{l}\cos x = \frac{{ - 1}}{2}\\\sin \left( {2x - \frac{\pi }{4}} \right) = 0\end{array} \right.\)

⇔ \(\left[ \begin{array}{l}x = \pm \frac{{2\pi }}{3} + k2\pi \\2x - \frac{\pi }{4} = k\pi \end{array} \right.\)

⇔ \(\left[ \begin{array}{l}x = \pm \frac{{2\pi }}{3} + k2\pi \\x = \frac{\pi }{8} + k\frac{\pi }{2}\end{array} \right.\left( {k \in \mathbb{Z}} \right)\).