This is a mathematical
tool for transforming trigonometric identities
into corresponding hyperbolic
Start with a standard identity, and multiply out fully in terms of sines
. Then replace the functions with their hyperbolic analogues. Finally, reverse the sign of any term involving sinh2
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).
sinh(3x) = 3cosh2(x)sinh(x) + sinh3(x).