Hyperbolic Equation

[Stormin63]

Hi,

i need to to prove that the real solution of

tanh x = cosech x


can be written in the form x = ln ( y +/- sqrt(y) )

i know tanh = (e^x - e^-x) / (e^x + e^-x) and cosech x = 2 / (e^x - e^-x)

Should I simply substitute these in and then it falls out of that?

Or should I stick to the sinh's etc to start with.

any help much appreciated.

 

[stapel]

What are the exponential definitions of these hyperbolic functions? Does anything helpful happen if you plug the solution value into those exponential expressions?