Google
Câu hỏi: Tập nghiệm của phương trình $\sin 2x=\sin x$ là
A. $S=\left\{ \left. k2\pi ;\dfrac{\pi }{3}+k2\pi \right|k\in \mathbb{Z} \right\}.$
B. $S=\left\{ \left. k2\pi ;\dfrac{\pi }{3}+\dfrac{k2\pi }{3} \right|k\in \mathbb{Z} \right\}.$
C. $S=\left\{ \left. k2\pi ;-\dfrac{\pi }{3}+k2\pi \right|k\in \mathbb{Z} \right\}.$
D. $S=\left\{ \left. k2\pi ;\pi +k2\pi \right|k\in \mathbb{Z} \right\}.$
A. $S=\left\{ \left. k2\pi ;\dfrac{\pi }{3}+k2\pi \right|k\in \mathbb{Z} \right\}.$
B. $S=\left\{ \left. k2\pi ;\dfrac{\pi }{3}+\dfrac{k2\pi }{3} \right|k\in \mathbb{Z} \right\}.$
C. $S=\left\{ \left. k2\pi ;-\dfrac{\pi }{3}+k2\pi \right|k\in \mathbb{Z} \right\}.$
D. $S=\left\{ \left. k2\pi ;\pi +k2\pi \right|k\in \mathbb{Z} \right\}.$
Ta có $\sin 2x=\sin x\Leftrightarrow \left[ \begin{aligned}
& 2x=x+k2\pi \\
& 2x=\pi -x+k2\pi \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& x=k2\pi \\
& x=\dfrac{\pi }{3}+\dfrac{k2\pi }{3} \\
\end{aligned} \right.\left( k\in \mathbb{Z} \right)$.
& 2x=x+k2\pi \\
& 2x=\pi -x+k2\pi \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& x=k2\pi \\
& x=\dfrac{\pi }{3}+\dfrac{k2\pi }{3} \\
\end{aligned} \right.\left( k\in \mathbb{Z} \right)$.
Đáp án B.