This is a mathematical tool for transforming trigonometric identities into corresponding hyperbolic ones.

Start with a standard identity, and multiply out fully in terms of sines and cosines. Then replace the functions with their hyperbolic analogues. Finally, reverse the sign of any term involving sinh2(x). For example, suppose we start with
cos2(x) + sin2(x) = 1.
The hyperbolic equivalent is therefore
cosh2(x) - sinh2(x) = 1.
A more complicated identity is
sin(3x) = 3cos2(x)sin(x) - sin3(x).
This becomes
sinh(3x) = 3cosh2(x)sinh(x) + sinh3(x).

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