Explanation Given information: cosh ( x + y ) , sinh ( x + y ) Formula used: sinh ( x + y ) = sinh x cosh y + cosh x sinh y cosh ( x + y ) = cosh x cosh y + sinh x sinh y Calculation: Put x = y in the above addition formulas to obtain Thus first consider the addition formula for sinh x sinh ( x + y ) = sinh x cosh y + cosh x sinh y When x = y it implies

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 1.6, Problem 46E

To determine

To prove using addition formula.

sinh(2x)=2coshxsinhxcosh(2x)=cosh2x+sinh2x

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Chapter 1.6, Problem 45E

Chapter 1.6, Problem 47E

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Chapter 1 Solutions

Calculus: Early Transcendentals

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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To prove using addition formula. sinh ( 2 x ) = 2 cosh x sinh x cosh ( 2 x ) = cosh 2 x + sinh 2 x

Solution Summary: The author explains how to prove using addition formulas by putting x=y in the formula.

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To prove using addition formula.

sinh(2x)=2coshxsinhxcosh(2x)=cosh2x+sinh2x

Want to see the full answer?

Chapter 1 Solutions

To prove using addition formula. sinh ( 2 x ) = 2 cosh x sinh x cosh ( 2 x ) = cosh 2 x + sinh 2 x

Solution Summary: The author explains how to prove using addition formulas by putting x=y in the formula.

Concept explainers

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To prove using addition formula. sinh(2x)=2coshxsinhxcosh(2x)=cosh2x+sinh2x

Want to see the full answer?

Chapter 1 Solutions

To prove using addition formula.

sinh(2x)=2coshxsinhxcosh(2x)=cosh2x+sinh2x