Đáp án:
Giải thích các bước giải:
`sin\ x=\sin\ \frac{2x}{3}`
`⇔` \(\left[ \begin{array}{l}x=\dfrac{2x}{3}+k2\pi\ (k \in \mathbb{Z})\\x=\pi-\dfrac{2x}{3}+k2\pi\ (k \in \mathbb{Z})\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}\dfrac{1}{3}x=k2\pi\ (k \in \mathbb{Z})\\\dfrac{5}{3}x=\pi+k2\pi\ (k \in \mathbb{Z})\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=k6\pi\ (k \in \mathbb{Z})\\x=\dfrac{3}{5}\pi+k\dfrac{6}{5}\pi\ (k \in \mathbb{Z})\end{array} \right.\)
Vậy `S={k6\pi\ (k \in \mathbb{Z});\frac{3}{5}\pi+k\frac{6}{5}\pi\ (k \in \mathbb{Z})}`