a) Explanation Given: An identity as sech 2 x + tanh 2 x = 1 Calculation: Let us consider sech 2 x + tanh 2 x and substitute the exponential values as shown: sech 2 x + tanh 2 x = ( 2 e x + e − x ) 2 + ( e x − e − x e x + e − x ) 2 = ( 2 e x + e − x ) ( 2 e x + e − x ) + ( e x − e − x e x + e − x ) ( e x − e − x e x + e − x ) = 4 e x e x + e − x e x + e − x e x + e − x e − x + e x e x − e − x e x − e − x e x + e</ b) To determine To prove: that coth 2 x − csch 2 x = 1

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 7.8, Problem 56PS

To determine

To prove: that sech2x+tanh2x=1 .

To determine

To prove: that coth2x−csch2x=1

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Chapter 7.8, Problem 55PS

Chapter 7.8, Problem 57PS

Chapter 7 Solutions

Calculus

Ch. 7.1 - Prob. 1PS Ch. 7.1 - Prob. 2PS Ch. 7.1 - Prob. 3PS Ch. 7.1 - Prob. 4PS Ch. 7.1 - Prob. 5PS Ch. 7.1 - Prob. 6PS Ch. 7.1 - Prob. 7PS Ch. 7.1 - Prob. 8PS Ch. 7.1 - Prob. 9PS Ch. 7.1 - Prob. 10PS

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To prove: that sech 2 x + tanh 2 x = 1 .

Solution Summary: The author explains how to calculate the exponential values of mathrmsech2x+