Answer
$ y $ is continuous on
$$...\cup(-\frac{3\pi}{2},-\frac{\pi}{2})\cup (-\frac{\pi}{2},\frac{\pi}{2})\cup(\frac{\pi}{2},\frac{3\pi}{2}) \cup(\frac{3\pi}{2},\frac{5\pi}{2})\cup(\frac{5\pi}{2},\frac{7\pi}{2})\cup...$$
Work Step by Step
Given $$ y=\frac{x+2}{\cos x} $$
Since the of the denominator is zero at
$\cos x=0 \Rightarrow x=\frac{\pi}{2}+k \pi, \ \ k \in Z $
So, $ y $ is continuous on
$$...\cup(-\frac{3\pi}{2},-\frac{\pi}{2})\cup (-\frac{\pi}{2},\frac{\pi}{2})\cup(\frac{\pi}{2},\frac{3\pi}{2}) \cup(\frac{3\pi}{2},\frac{5\pi}{2})\cup(\frac{5\pi}{2},\frac{7\pi}{2})\cup...$$