Answer
$x=-\frac{3\pi}{2},-\frac{\pi}{2},\frac{\pi}{2},\frac{3\pi}{2}$
Work Step by Step
If $x=-\frac{3\pi}{2},-\frac{\pi}{2},\frac{\pi}{2},\frac{3\pi}{2}$, $\sec{x}=\frac{1}{\cos{x}}$ has vertical asymptotes because $\cos{x}=0$ at those values, hence the denominator is $0$, therefore $\sec{x}$ is undefined at those values. (see graph)
