Answer
$\sec^{-1}0$ is not defined.
Work Step by Step
Inverse Secant Function:
$y=\sec^{-1}x$ or $y=$ arcsec $x$ means that
$x=\sec y$, for $0 \leq y \leq \pi, y\displaystyle \neq\frac{\pi}{2}$.
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The secant function is reciprocal to the cosine.
There is no y from the interval $0 \leq y \leq \pi, y\displaystyle \neq\frac{\pi}{2}$
such that
$\displaystyle \sec y=\frac{1}{\cos y}=0$
(the reciprocal of 0 does not exist)
So,
$\sec^{-1}0$ is not defined.
