Chapter 2: Differentiation
Section 2.9: The Hyperbolic Functions and Their Derivatives
Verify the first hyperbolic Pythagorean identity in Table 2.9.5.
As in Example 2.9.1, verification of the (hyperbolic) Pythagorean, addition, and double-angle identities is effected by replacing each hyperbolic function with its exponential equivalent. Think of this approach as the eeezy way. Verification of the Pythagorean identity is as follows.
=14e2 x+2ex−x+e−2 x−14e2 x−2ex−x+e−2 x
=14e2 x−e2 x+2e0+2e0+e−2 x−e−2 x
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