Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - Summary Exercises Verifying Trigonometric Identities - Exercises: 15

Answer

$\cos x=\dfrac {1-\tan ^{2}\dfrac {x}{2}}{1+\tan ^{2}\dfrac {x}{2}}$

Work Step by Step

$\cos x=\cos ^{2}\dfrac {x}{2}-\sin ^{2}\dfrac {x}{2}=\left( \dfrac {1}{\sqrt {1+\tan ^{2}\dfrac {x}{2}}}\right) ^{2}-\left( \dfrac {\tan \dfrac {x}{2}}{\sqrt {1+\tan ^{2}\dfrac {x}{2}}}\right) ^{2}=\dfrac {1-\tan ^{2}\dfrac {x}{2}}{1+\tan ^{2}\dfrac {x}{2}}$
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