Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.4 - Product-to-Sum and Sum-to-Product Formulas - Exercise Set - Page 689: 31


a. $y=cos(x)$ b. see explanations.

Work Step by Step

a. The graph appears to be the same as $y=cos(x)$ b. Using the addition and double-angle formulas, we have $y=\frac{sin(x)+sin(2x+x)}{2sin(2x)}=\frac{sin(x)+sin(2x)cos(x)+cos(2x)sin(x)}{4sin(x)cos(x)}=\frac{sin(x)+2sin(x)cos^2(x)+cos(2x)sin(x)}{4sin(x)cos(x)}=\frac{1+2cos^2(x)+cos(2x)}{4cos(x)}=\frac{1+2cos^2(x)+2cos^(x)-1}{4cos(x)}=cos(x)$
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