ĐKXĐ: \(\cos 2x\ne 0\), \(\sin x\ne 0\) và \(\cos x\ne 0\)
\(\Leftrightarrow \cos 2x\ne 0\) và \(\sin 2x\ne 0\)
\(\Leftrightarrow \sin 4x\ne 0\)
\(\Leftrightarrow 4x\ne k\pi ,k\in\mathbb{Z}\)
\(\Leftrightarrow x\ne k\dfrac{\pi}{4} ,k\in\mathbb{Z}\)
Ta có: \(3\tan 2x+6\cot x=-\tan x\)
\(\Leftrightarrow 3\dfrac{2\tan x}{1-{tan}^2 x}+\dfrac{6}{\tan x}+\tan x=0\)
\(\Leftrightarrow 6{\tan}^2 x+6-6{\tan}^2 x+{\tan}^2 x(1-{\tan}^2 x)=0\)
\(\Leftrightarrow -{\tan}^4 x+{\tan}^2 x+6=0\)
\(\Leftrightarrow \left[ \begin{array}{l} {\tan}^2 x = -2<0\text{(loại)}\\{\tan}^2 x= 3\end{array} \right. \)
\(\Leftrightarrow \tan x = \pm\sqrt{3}\)
\(\Leftrightarrow x = \pm\dfrac{\pi}{3}+k\pi ,k \in \mathbb{Z}\)
Đáp án: B.
