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: 10

Answer

cosh(x) - sinh(x) = $e^{-x}$

Work Step by Step

Use the definition of the hyperbolical sine and cosine and do a simple fraction subtraction. $$sinh(x) = \frac{e^{x} - e^{-x}}{2}$$ $$cosh(x) = \frac{e^{x} + e^{-x}}{2}$$ cosh(x) - sinh(x) = $\frac{e^{x} + e^{-x}}{2}$ - $\frac{e^{x} - e^{-x}}{2}$ = $\frac{2e^{-x}}{2}$ = $e^{-x}$
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