Manipulating hyperbolic functions

[pokgai]

Homework Statement

Express the function cosh(6x) in terms of powers of cosh(x)

Homework Equations

The Attempt at a Solution

Okay the problem booklet also asks me to do the opposite. Express cosh(x)^6 as mutiples of cosh(x). I can do that fine, I just simply write it out as [1/2(e^x + e^-x)]^6 etc. and then expand using pascals and group the like terms and that gives me multiples.

However I have no idea where to begin when I'm doing the opposite. I assume I use double angle formulas as I have nothing else? hints would be appreciated

Cheers

 

[Dick]

cosh(a+b)=cosh(a)*cosh(b)+sinh(a)*sinh(b). 6x=3x+3x. Now work your way down to powers of cosh(x). Yes, there are multiple angle formulas. There's a similar one for sinh.