Calculus (3rd Edition)

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: 19



Work Step by Step

Assume that $\sec\theta =\frac{x}{1}$, then by solving the triangle, we have: $$\cot \theta=\frac{1}{\sqrt{x^2-1}}.$$ Now, since $\theta =\sec^{-1}x $, we have $$\cot(\sec^{-1}x)=\cot\theta=\frac{1}{\sqrt{x^2-1}}.$$
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