Answer
Undefined.
Work Step by Step
Since $\sec\left(\frac{3\pi}{2}\right)$ is undefined, then
$$\sec^{-1}\left(\sec\left(\frac{3\pi}{2}\right)\right)$$ is undefined.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Exercises - Page 374: 14
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