Điều kiện xác định:
$\begin{array}{l} \cos \left( {\dfrac{\pi }{2}\cos x} \right) \ne 0\\ \Leftrightarrow \dfrac{\pi }{2}\cos x \ne \dfrac{\pi }{2} + k\pi \\ \Leftrightarrow \cos x \ne 1 + 2k\\ \Rightarrow \left\{ \begin{array}{l} \cos x \ne 1\left( {k = 0} \right)\\ \cos x \ne - 1\left( {k = - 1} \right) \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} x \ne k2\pi \\ x \ne \pi + k2\pi \end{array} \right. \Rightarrow x \ne k\pi \\ \Rightarrow D = \mathbb{R}\backslash \left\{ {k\pi |k \in \mathbb{Z}} \right\} \end{array}$
