Answer
$\frac{\pi}{2} -2$
Work Step by Step
We know that $\cos(x) = \sin(\frac{\pi}{2}-x)$. This means that $\sec(2) = \frac{1}{\cos(2)} = \frac{1}{\sin(\frac{\pi}{2}-2)} = \csc(\frac{\pi}{2}-2)$. Substituting this into the original equation, we have: $\csc^{-1}(\sec(2)) = \csc^{-1}(\csc(\frac{\pi}{2}-2)) = \frac{\pi}{2} -2$
