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: 33


a. $y=tan(2x)$ b. see explanations.

Work Step by Step

a. It appears that the function $y=tan(2x)$ gives the same graph. b. Using the sum to product formula, we have $cos(x)-cos(5x)=-2sin(\frac{x+5x}{2}) sin(\frac{x-5x}{2})=2sin(3x) sin(2x)$ and $sin(x)+sin(5x)=2sin(\frac{x+5x}{2}) cos(\frac{x-5x}{2})=2sin(3x) cos(2x)$ Thus we have $y=\frac{cos(x)-cos(5x)}{sin(x)+sin(5x)}=\frac{2sin(3x) sin(2x)}{2sin(3x) cos(2x)}=tan(2x)$
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