$\begin{array}{l}
\left\{ \begin{array}{l}
\cos x \ne 0\\
1 + \tan x \ne 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\cos x \ne 0\\
\tan x \ne - 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \ne \dfrac{\pi }{2} + k\pi \\
x \ne - \dfrac{\pi }{4} + k\pi
\end{array} \right.\left( {k \in \mathbb Z} \right)\\
D = \mathbb R\backslash \left\{ {\dfrac{\pi }{2} + k\pi , - \dfrac{\pi }{4} + k\pi ,k \in \mathbb Z} \right\}
\end{array}$
