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: 24


$$\frac{1}{\sqrt 2}$$

Work Step by Step

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