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:

sin^{2}(½Θ) = ½(1 - cos(Θ))
cos^{2}(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,

sinh^{2}(½Θ) = ½(cosh(Θ) - 1)
cosh^{2}(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**.