University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 7 - Section 7.3 - Hyperbolic Functions - Exercises - Page 417: 10



Work Step by Step

We apply hyperbolic function formulas: $ \cosh x= \dfrac{e^x+e^{-x}}{2}$ and $ \sinh x= \dfrac{e^x-e^{-x}}{2}$ Thus, $\ln (\cosh x+\sinh x )+ \ln (\cosh x -\sinh x )=\ln [\dfrac{e^x+e^{-x}}{2}+\dfrac{e^x-e^{-x}}{2}]+\ln [\dfrac{e^x+e^{-x}}{2} -\dfrac{e^x-e^{-x}}{2}]=\ln [\dfrac{2e^x}{2}] + \ln [\dfrac{2e^{-x}}{2}]=x-x=0$
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