Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.4 - Sum and Difference Equations - 7.4 Exercises - Page 539: 64


The identity is verified. $cos(x+y)~cos(x-y)=cos^2x-sin^2y$

Work Step by Step

$cos(u+v)=cos~u~cos~v-sin~u~sin~v$ $cos(u-v)=cos~u~cos~v+sin~u~sin~v$ $cos^2x+sin^2x=1$ $cos^2x=1-sin^2x$ $sin^2x=1-cos^2x$ $cos(x+y)~cos(x-y)=(cos~x~cos~y-sin~x~sin~y)(cos~x~cos~y+sin~x~sin~y)=cos^2~x~cos^2~y-sin^2~x~sin^2~y=cos^2x(1-sin^2y)-(1-cos^2x)sin^2y=cos^2x-cos^2x~sin^2y-sin^2y+cos^2xsin^2y=cos^2x-sin^2y$
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