Hyperbolic Functions 1
? Maplesoft, a division of Waterloo Maple Inc., 2007
Introduction
This application is one of a collection of examples teaching Calculus with Maple. These applications use Clickable Calculus? methods to solve problems interactively. Steps are given at every stage of the solution, and many are illustrated using short video clips. Click on the
buttons to watch the videos.
The steps in the document can be repeated to solve similar problems.
Problem Statement
Verify the identity 
.
Solution
There are three possible methods of verifying this identity: from first principles, using Maple operators and using the test relation option in the Context Menu.
Step
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Result
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Enter  and convert it to exponential form.
Enter  and press [Enter]. Right-click, Conversions>Exponential.
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(3.1) |
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(3.2) |
|
Square the exponential form of  .
Use the equation label to enter the appropriate expression ([Ctrl]+L, enter the equation number, [Enter]). Right-click, Expand.
|
 |
(3.3) |
 |
(3.4) |
|
Enter  and convert it to exponential form.
Enter  and press [Enter]. Right-click, Conversions>Exponential.
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(3.5) |
 |
(3.6) |
|
Square the exponential form of  .
Use the equation label to enter the appropriate expression ([Ctrl]+L, enter the equation number, [Enter]). Right-click, Expand.
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(3.7) |
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(3.8) |
|
Construct the left-hand side of the identity and verify that this is the same as the right-hand side.
Use the equation labels to enter the expression. Press [Enter] to evaluate.
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(3.9) |
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Additional Methods
Enter the expression for the left-hand side of the identity in the form  .
Use the equation labels for  and  to enter the expression.
Right-click: Combine>Trig.
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(3.10) |
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(3.11) |
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Enter the expression for the identity.
Use the equation labels for  and  to construct the identity. Press [Enter].
Right-click: Test Relation.
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(3.12) |
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(3.13) |
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