Đáp án:$\left[ \begin{array}{l}
a \ge 2\\
x \le 0
\end{array} \right.$
Giải thích các bước giải:
$\begin{array}{l}
\cos x = \frac{1}{{a - 1}}\\
\Rightarrow \left\{ \begin{array}{l}
a \ne 1\\
- 1 \le \frac{1}{{a - 1}} \le 1
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a \ne 1\\
1 + \frac{1}{{a - 1}} \ge 0\\
\frac{1}{{a - 1}} - 1 \le 0
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
a \ne 1\\
\frac{{a - 1 + 1}}{{a - 1}} \ge 0\\
\frac{{1 - a + 1}}{{a - 1}} \le 0
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
a \ne 1\\
\frac{a}{{a - 1}} \ge 0\\
\frac{{a - 2}}{{a - 1}} \ge 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a \ne 1\\
\left[ \begin{array}{l}
a \ge 2\\
a \le 0
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
a \ge 2\\
x \le 0
\end{array} \right.
\end{array}$
