EXAMPLE 1 Prove (a) cosh?(x) – sinh?(x) = 1 and (b) 1- tanh?(x) = sech?(x). %3D SOLUTION (a) cosh°(x) – sinh (x) = ( *** -(| 2 e2x + 2 + e-2x 4 4 (b) We start with the identity proved in part (a): cosh (x) – sinh (x) = 1. If we divide both sides by cosh?(x), we get 1 sinh?(x) 1 cosh?(x) 1- tanh?(x) or
EXAMPLE 1 Prove (a) cosh?(x) – sinh?(x) = 1 and (b) 1- tanh?(x) = sech?(x). %3D SOLUTION (a) cosh°(x) – sinh (x) = ( *** -(| 2 e2x + 2 + e-2x 4 4 (b) We start with the identity proved in part (a): cosh (x) – sinh (x) = 1. If we divide both sides by cosh?(x), we get 1 sinh?(x) 1 cosh?(x) 1- tanh?(x) or
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![EXAMPLE 1 Prove (a) cosh?(x) – sinh?(x) = 1 and (b) 1- tanh?(x) = sech?(x).
SOLUTION
(a) cosh°(x) – sinh (x) = ( -(|
2.
e2x + 2 + e-2x
4
4
(b) We start with the identity proved in part (a):
cosh (x) – sinh?(x) = 1.
If we divide both sides by cosh2(x), we get
sinh?(x)
cosh?(x)
1 -
1- tanh?(x) =
or](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F030351ce-7395-4d65-a8bf-32d9b407aff1%2F17024fcb-a380-4919-85b9-17a796c8a6f8%2Fzta5bb_processed.png&w=3840&q=75)
Transcribed Image Text:EXAMPLE 1 Prove (a) cosh?(x) – sinh?(x) = 1 and (b) 1- tanh?(x) = sech?(x).
SOLUTION
(a) cosh°(x) – sinh (x) = ( -(|
2.
e2x + 2 + e-2x
4
4
(b) We start with the identity proved in part (a):
cosh (x) – sinh?(x) = 1.
If we divide both sides by cosh2(x), we get
sinh?(x)
cosh?(x)
1 -
1- tanh?(x) =
or
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