Explanation Given information: We must show that: cosh ( x + y ) = cosh x cosh y + sinh x sinh y Formula used: Hyperbolic function of cos x and sin x : cosh x = e x + e − x 2 sinh x = e x − e − x 2 Proof: To show: cosh ( x + y ) = cosh x cosh y + sinh x sinh y Take Right hand side cosh ( x ) ⋅ cosh ( y ) + sinh ( x ) ⋅ sinh ( y ) = [ e x + e − x 2 ] ⋅ [ e y + e − y 2 ] + [ e x − e − x 2 ] [ e y − e − y 2 ] = [ ( e x + y + e x − y

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 1.6, Problem 45E

To determine

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cosh(x+y)=coshxcoshy+sinhxsinhy

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Chapter 1.6, Problem 44E

Chapter 1.6, Problem 46E

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Chapter 1 Solutions

Calculus: Early Transcendentals

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Toprove: cosh ( x + y ) = cosh x cosh y + sinh x sinh y

Solution Summary: The author analyzes the hyperbolic function of mathrmcosx and

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Toprove:

cosh(x+y)=coshxcoshy+sinhxsinhy

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Chapter 1 Solutions

Toprove: cosh ( x + y ) = cosh x cosh y + sinh x sinh y

Solution Summary: The author analyzes the hyperbolic function of mathrmcosx and

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Toprove: cosh(x+y)=coshxcoshy+sinhxsinhy

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Chapter 1 Solutions

Toprove:

cosh(x+y)=coshxcoshy+sinhxsinhy