A set of formulae expressing trigonometric functions of an angle x in terms of an angle 2x,
Personally I think it is a lot easier to simply use the Double Angle Formulae in reverse, as opposed to remembering a new set of formulae which are ultimately redundant. However, for those who like pain, here we are:
sin2(½Θ) = ½(1 - cos(Θ))
cos2(½Θ) = ½(1 + cos(Θ))
sin(Θ)
tan(½Θ) = ----------
1 + cos(Θ)
1 - cos(Θ)
= ----------
sin(Θ)
tan(Θ)sin(Θ)
= --------------
tan(Θ) + sin(Θ)
Through the use of Osborne's rule we can arrive at the corresponding set of formulae for hyperbolic functions,
sinh2(½Θ) = ½(cosh(Θ) - 1)
cosh2(½Θ) = ½(cosh(Θ) + 1)
sinh(Θ)
tanh(½Θ) = ------------
cosh(Θ) + 1
cosh(Θ) - 1
= ------------
sinh(Θ)
To reverse the process you may use the Double Angle Formulae.