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Chapter 1 | Functions and Graphs
Figure 1.51 The hyperbolic functions involve combinations of e x and e − x .
Identities Involving Hyperbolic Functions The identity cosh 2 t −sinh 2 t , shown in Figure 1.50 , is one of several identities involving the hyperbolic functions, some of which are listed next. The first four properties follow easily from the definitions of hyperbolic sine and hyperbolic cosine. Except for some differences in signs, most of these properties are analogous to identities for trigonometric functions.
Rule: Identities Involving Hyperbolic Functions 1. cosh(− x ) =cosh x 2. sinh(− x ) =−sinh x 3. cosh x +sinh x = e x 4. cosh x −sinh x = e − x
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