Answer
The identity is verified.
$cos^4-sin^4x=cos~2x$
Work Step by Step
Use: $cos^2x+sin^2x=1$ and $cos~2x=cos^2x-sin^2x$
Start on the left side:
$cos^4-sin^4x=(cos^2x)^2-(sin^2x)^2=(cos^2x+sin^2x)(cos^2x-sin^2x)=(1)~(cos~2x)=cos~2x$
Algebra and Trigonometry 10th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
9781337271172
ISBN 13:
978-1-33727-117-2
Chapter 7 - Review Exercises - Page 553: 66
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