Explanation Given information: tanh ( u + v ) Formula used: sinh ( u + v ) = sinh u cosh v + cosh u sinh v cosh ( u + v ) = cosh u cosh v + sinh u sinh v Calculation: The addition identities for hyperbolic sine and cosine are. sinh ( u + v ) = sinh u cosh v + cosh u sinh v cosh ( u + v ) = cosh u cosh v + sinh u sinh v Dividing these will give us the following relation. tanh ( u + v ) = sinh u cosh v + cosh u sinh v cosh u cosh v + sinh u sinh v We can simplify this relation by dividing both the numerator and the denominator by cosh u cos v and simplifying

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 1.6, Problem 51E

To determine

To prove:

tanh(u+υ)=tanhu+tanhυ1+tanhutanhυ by using the addition formulas.

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Chapter 1.6, Problem 50E

Chapter 1.6, Problem 52E

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Chapter 1 Solutions

Calculus: Early Transcendentals

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To prove: tanh ( u + υ ) = tanh u + tanh υ 1 + tanh u tanh υ by using the addition formulas.

Solution Summary: The author calculates the addition identities for hyperbolic sine and cosine by using addition formulas.

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To prove:

tanh(u+υ)=tanhu+tanhυ1+tanhutanhυ by using the addition formulas.

Want to see the full answer?

Chapter 1 Solutions

To prove: tanh ( u + υ ) = tanh u + tanh υ 1 + tanh u tanh υ by using the addition formulas.

Solution Summary: The author calculates the addition identities for hyperbolic sine and cosine by using addition formulas.

Concept explainers

Videos

To prove: tanh(u+υ)=tanhu+tanhυ1+tanhutanhυ by using the addition formulas.

Want to see the full answer?

Chapter 1 Solutions

To prove:

tanh(u+υ)=tanhu+tanhυ1+tanhutanhυ by using the addition formulas.