Đáp án:
$\begin{array}{l}
\dfrac{1}{{\sqrt {\left| {{\mathop{\rm tanx}\nolimits} + cotx} \right| - 1,999} }}\\
Dkxd:\left\{ \begin{array}{l}
\cos x \ne 0\\
\sin x \ne 0\\
\left| {{\mathop{\rm tanx}\nolimits} + cotx} \right| > 1,999
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x \ne \dfrac{\pi }{2} + k\pi \\
x \ne k\pi \\
\left| {\dfrac{{\sin x}}{{\cos x}} + \dfrac{{\cos x}}{{\sin x}}} \right| > 1,999
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x \ne \dfrac{{k\pi }}{2}\\
\left| {\dfrac{1}{{\cos x.\sin x}}} \right| > 1,999
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x \ne \dfrac{{k\pi }}{2}\\
\dfrac{1}{{\left| {2\sin x.\cos x} \right|}} > \dfrac{{1,999}}{2}
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x \ne \dfrac{{k\pi }}{2}\\
\left| {\sin 2x} \right| < 1,00005\left( {\text{luôn}\,\text{đúng}} \right)
\end{array} \right.\\
\Rightarrow x \ne \dfrac{{k\pi }}{2}
\end{array}$
