Câu 24 :
Ta có : \(\sin\left(x+\dfrac{\pi}{3}\right)-\sin x=0\)
\(\Leftrightarrow2\cos\left(\dfrac{x+\dfrac{\pi}{3}+x}{2}\right)\sin\left(\dfrac{x+\dfrac{\pi}{3}-x}{2}\right)=0\)
\(\Leftrightarrow\cos\left(x+\dfrac{\pi}{6}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{\pi}{6}=\dfrac{\pi}{2}+k2\pi\\x+\dfrac{\pi}{6}=\dfrac{3}{2}\pi+k2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{3}+k2\pi\\x=\dfrac{4}{3}\pi+k2\pi\end{matrix}\right.\)
Mà \(0< x< 2\pi\)
\(\Rightarrow k=0\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{3}\\x=\dfrac{4}{3}\pi\end{matrix}\right.\)
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