Double Angle Formulae (idea)

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) = cos2(x) - sin2(x)
            = 2.cos2(x) - 1
            = 1 - 2.sin2(x)

               2.tan(x)
    tan(2x) = -----------
              1 - tan2(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) = cosh2(x) + sinh2(x)
             = 2.cosh2(x) - 1
             = 1 + 2.sinh2(x)

               2.tanh(x)
    tan(2x) = ------------
              1 + tanh2(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.