**Hyperbolic functions - Wikipedia**
https://en.wikipedia.org/wiki/Hyperbolic_functions

Hyperbolic tangent. The hyperbolic tangent is the (unique) solution to the differential equation f ′ = 1 − f 2, with f (0) = 0.. Useful relations. The hyperbolic functions satisfy many identities, all of them similar in form to the trigonometric identities.In fact, Osborn's rule states that one can convert any trigonometric identity for , , or and into a hyperbolic identity, by expanding ...

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