   Chapter 3.11, Problem 18E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Prove the identity.18. 1 + tanh x 1 − tanh x = e 2 x

To determine

To prove: The identity 1+tanhx1tanhx=e2x.

Explanation

Definition used:

(1) The hyperbolic sine function sinhx=exex2.

(2) The hyperbolic cosine function coshx=ex+ex2.

(3) The hyperbolic tangent function tanhx=sinhxcoshx.

Proof:

Consider 1+tanhx1tanhx.

Use definition (3) and simplify further.

1+tanhx1tanhx =1+sinhxcoshx1sinhxcoshx=coshx+sinhxcoshxcoshxsinhxcoshx=coshx+sinhxcoshxsinhx

Use the definition (1) and (2),

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