Algebra and Trigonometry 10th Edition

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

Chapter 7 - 7.5 - Multiple-Angle and Product-to-Sum Formulas - 7.5 Exercises - Page 549: 69


The identity is verified. $\frac{sin~x±sin~y}{cos~x+cos~y}=tan\frac{x±y}{2}$

Work Step by Step

$\frac{sin~x+sin~y}{cos~x+cos~y}=\frac{2~sin(\frac{x+y}{2})~cos(\frac{x-y}{2})}{2~cos(\frac{x+y}{2})~cos(\frac{x-y}{2})}=\frac{sin(\frac{x+y}{2})}{cos(\frac{x+y}{2})}=tan\frac{x+y}{2}$ $\frac{sin~x-sin~y}{cos~x+cos~y}=\frac{2~cos(\frac{x+y}{2})~sin(\frac{x-y}{2})}{2~cos(\frac{x+y}{2})~cos(\frac{x-y}{2})}=\frac{sin(\frac{x-y}{2})}{cos(\frac{x-y}{2})}=tan\frac{x-y}{2}$
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