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Osborn's Rule


The prescription that a trigonometry identity can be converted to an analogous identity for hyperbolic functions by expanding, exchanging trigonometric functions with their hyperbolic counterparts, and then flipping the sign of each term involving the product of two hyperbolic sines. For example, given the identity

 cos(x-y)=cosxcosy+sinxsiny,

Osborn's rule gives the corresponding identity

 cosh(x-y)=coshxcoshy-sinhxsinhy.

See also

Hyperbolic Functions, Trigonometric Functions

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References

Osborn, G. "Mnemonic for Hyperbolic Formulae." Math. Gaz. 2, 189, 1902.

Referenced on Wolfram|Alpha

Osborn's Rule

Cite this as:

Weisstein, Eric W. "Osborn's Rule." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OsbornsRule.html

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