Answer
$\frac{1}{|u|}$
Work Step by Step
1. Let $sec^{-1}u=t, 0\lt t\lt\pi$, we have $sec(t)=u$.
2. Let $r=|u|,x=1$, we have $y=\sqrt {u^2-1}$
3. Thus $cos(sec^{-1}u)=cos(t)=\frac{x}{r}=\frac{1}{|u|}$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 6 - Analytic Trigonometry - Section 6.2 The Inverse Trigonometric Functions (Continued) - 6.2 Assess Your Understanding - Page 481: 64
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