# Hyperbolic Functions

1. Apr 25, 2008

### hex.halo

1. The problem statement, all variables and given/known data

Given the trigonometric identity cos(x+y)... use Osborn's rule to write down the corresponding identity for cosh(x+y)... Use the definitionis of the hyperbolic functions to prove this identity

2. Relevant equations

3. The attempt at a solution

I can use Osborns rule to find the hyperbolic equivilent of the identity, however, I don't understand how I am to prove this identity...

2. Apr 25, 2008

### rock.freak667

$cos(x+y)=cosxcosy-sinxsiny$

Osborn said that when you have the product of two sines, you replace the sines with sinh and a negative sign.

so therefore $cosh(x+y)=cosxcosy-(-sinhxsinhy)$

3. Apr 26, 2008

### exk

rock.freak missed the h in his last bit for the 2 cos terms on the rhs.
$cosh(x+y)=coshxcoshy-(-sinhxsinhy)$

4. Apr 26, 2008

### HallsofIvy

Staff Emeritus
Okay, you already know that cosh(x+ y)= cosh(x)cosh(y)+ sinh(x)sinh(y). Now replace cosh(x) by $(e^x+ e^{-x})/2$, replace sinh(x)= [itex](e^x- e{-x})/2[/tex], the corresponding things for cosh(y) and sinh(y) and do the algebra. What do you get when you multiply
$$\frac{e^x+ e^{-x}}{2}\frac{e^y+ e^{-y}}{2}$$

Last edited: Apr 26, 2008