Điều kiện xác định
$\begin{array}{l} \cos x \ne 0,\,\sin x \ne 0\\ \Leftrightarrow \left\{ \begin{array}{l} x \ne \dfrac{\pi }{2} + k\pi \\ x \ne m\pi \end{array} \right.\left( {k,m \in \mathbb{Z}} \right) \end{array}$
$\begin{array}{l}
\left( {1 + {{\cot }^2}x} \right)\tan x = 2\\
\Leftrightarrow 1 + {\cot ^2}x = \dfrac{2}{{\tan x}} = 2.\dfrac{1}{{\tan x}} = 2\cot x\\
\Leftrightarrow {\cot ^2}x - 2\cot x + 1 = 0\\
\Leftrightarrow {\left( {\cot x - 1} \right)^2} = 0\\
\Leftrightarrow \cot x = 1\\
\Leftrightarrow \cot x = \cot \dfrac{\pi }{4}\\
\Leftrightarrow x = \dfrac{\pi }{4} + l\pi \left( {l \in \mathbb{Z}} \right)
\end{array}$
