Osborne'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

$$\cos(x-y)=\cos x\cos y+\sin x\sin y,$$

Osborne's rule gives the corresponding identity

$$\cosh(x-y)=\cosh x\cosh y-\sinh x\sinh y.$$

See also Hyperbolic Functions, Trigonometry