Chapter 1 - Functions - 1.4 Trigonometric Functions and Their Inverse - 1.4 Exercises - Page 48: 73

$\frac{\pi}{2} -2$

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: $\csc^{-1}(\sec(2)) = \csc^{-1}(\csc(\frac{\pi}{2}-2)) = \frac{\pi}{2} -2$