Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.11 - Hyperbolic Functions - 3.11 Exercises - Page 264: 15

Answer

$sinh~2x = 2~sinh~x~cosh~x$

Work Step by Step

$sinh~2x = \frac{e^{2x}-e^{-2x}}{2}$ $sinh~2x = \frac{(e^{x}-e^{-x})(e^x+e^{-x})}{2}$ $sinh~2x = \frac{2(e^{x}-e^{-x})(e^x+e^{-x})}{4}$ $sinh~2x = 2~\frac{e^{x}-e^{-x}}{2}\cdot \frac{e^x+e^{-x}}{2}$ $sinh~2x = 2~sinh~x~cosh~x$
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