Answer
$\frac{\sqrt 2}{2}$
Work Step by Step
The expression fit the cosine Double-Angle Formula $cos2\theta=cos^2\theta-sin^2\theta$, we have
$cos^2\frac{\pi}{8}-sin^2\frac{\pi}{8}=cos2(\frac{\pi}{8})=cos\frac{\pi}{4}=\frac{\sqrt 2}{2}$
Precalculus: Mathematics for Calculus, 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305071751
ISBN 13:
978-1-30507-175-9
Chapter 7 - Review - Exercises - Page 579: 55
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