A set of formulae expressing trigonometric functions of an angle **2x** in terms of an angle **x**,

sin(2x) = 2.sin(x)cos(x)
cos(2x) = cos^{2}(x) - sin^{2}(x)
= 2.cos^{2}(x) - 1
= 1 - 2.sin^{2}(x)
2.tan(x)
tan(2x) = -----------
1 - tan^{2}(x)

Through the use of **Osborne's rule** we can arrive at the corresponding set of formulae for hyperbolic functions,

sinh(2x) = 2.sinh(x)cosh(x)
cosh(2x) = cosh^{2}(x) + sinh^{2}(x)
= 2.cosh^{2}(x) - 1
= 1 + 2.sinh^{2}(x)
2.tanh(x)
tan(2x) = ------------
1 + tanh^{2}(x)

To reverse the process is trivial, however if you like paining yourself with redundant formulae you may use the **Half Angle Formulae** for this purpose.