`~rai~`
\(\dfrac{\sqrt{3}\sin x-\cos x-1}{\sin3x}=0\quad(1)\\ĐKXĐ:\sin3x\ne 0\\\Leftrightarrow 3x\ne k\pi\\\Leftrightarrow x\ne k\dfrac{\pi}{3}.(k\in\mathbb{Z})\\(1)\Leftrightarrow \sqrt{3}\sin x-\cos x-1=0\\\Leftrightarrow \sqrt{3}\sin x-\cos x=1\\\Leftrightarrow \dfrac{\sqrt{3}}{2}\sin x-\dfrac{1}{2}\cos x=\dfrac{1}{2}\\\Leftrightarrow \sin\left(x-\dfrac{\pi}{6}\right)=\dfrac{1}{2}\\\Leftrightarrow \left[\begin{array}{I}x-\dfrac{\pi}{6}=\dfrac{\pi}{6}+k2\pi\\x-\dfrac{\pi}{6}=\pi-\dfrac{\pi}{6}+k2\pi\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}x=\dfrac{\pi}{3}+k2\pi\\x=\pi+k2\pi.\end{array}\right.\quad(k\in\mathbb{Z})\\\text{Kết hợp nghiệm và ĐKXĐ trên đường tròn lượng giác}\\\Rightarrow \text{Phương trình vô nghiệm.}\\\to\text{Chọn ý A.}\)
