Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises: 26

Answer

$\dfrac {\cos \dfrac {\pi }{4}}{2}=\dfrac {\sqrt {2}}{4}$

Work Step by Step

$2\cos ^{2}\alpha -1=\cos ^{2}\alpha \Rightarrow \cos ^{2}\dfrac {\pi }{8}-\dfrac {1}{2}=\dfrac {2\cos ^{2}\dfrac {\pi }{8}-1}{2}=\dfrac {\cos \left( 2\times \dfrac {\pi }{8}\right) }{2}=\dfrac {\cos \dfrac {\pi }{4}}{2}=\dfrac {\sqrt {2}}{4}$
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