ĐKXĐ: \(\sin x\ne 0\)
\(\Leftrightarrow x\ne k\pi ,k\in\mathbb{Z}\)
Ta có: \(2\sin x=3\cot x\)
\(\Leftrightarrow 2\sin x=3\dfrac{\cos x}{\sin x}\)
\(\Leftrightarrow 2{\sin}^2 x=3\cos x\)
\(\Leftrightarrow 2(1-{\cos}^2 x)-3\cos x=0\)
\(\Leftrightarrow 2{\cos}^2 x+3\cos x-2=0\)
\(\Leftrightarrow \left[ \begin{array}{l} \cos x = -2<-1\text{(loại)}\\\cos x= \dfrac{1}{2}\end{array} \right. \)
\(\Leftrightarrow x = \pm\dfrac{\pi}{3}+k2\pi ,k \in \mathbb{Z}\text{(thỏa mãn)}\)
Đáp án: D.
