Điều kiện xác định:
$\left\{ \begin{array}{l}
\sin 2x \ne 0\\
\sin x \ne 0
\end{array} \right. \Rightarrow \sin 2x \ne 0 \Leftrightarrow 2x \ne k\pi \Leftrightarrow x \ne \dfrac{{k\pi }}{2}$
$\cot x - \tan x = \dfrac{{\cos x}}{{\sin x}} - \dfrac{{\sin x}}{{\cos x}} = \dfrac{{\cos 2x}}{{\dfrac{1}{2}\sin 2x}} = 2\cot 2x$
$\begin{array}{l}
\cot 2x - 2\cot x = 0\\
\Leftrightarrow \dfrac{1}{2}\cot x - \dfrac{1}{2}\tan x - 2\cot x = 0\\
\Leftrightarrow - \dfrac{3}{2}\cot x - \dfrac{1}{2}\tan x = 0\\
\Leftrightarrow \dfrac{3}{2}\cot x + \dfrac{1}{2}\tan x = 0\\
\Leftrightarrow \dfrac{3}{{2\tan x}} + \dfrac{1}{2}\tan x = 0\\
\Leftrightarrow {\tan ^2}x + 3 = 0\\
\to PTVN\\
\Rightarrow S = \emptyset
\end{array}$
