How to write this expression in terms of a Hyperbolic function?

[Safinaz]

Homework Statement

How to write this expression in terms of a Hyperbolic function

Relevant Equations

How to write :

##
Eq= e^{t ( -h \pm \sqrt{ x} )}
##

I terms of ##Cosh (x) = e^x + e^{-x} /2 ##

The eqution can be written as:

##
Eq= e^{t( -h + \sqrt{ x} )} + e^{t( -h -\sqrt{ x} )}
##

Can this be written in terms of Cosh x ?

 

[PeroK]

It could be written in terms of ##\cosh \sqrt x##.

 

[Safinaz]

It could be written in terms of ##\cosh \sqrt x##.

So can it written as:

## Eq = e^{ -ht} ( e^{t\sqrt{x}} + e^{-t\sqrt{x}} ) = 2 e^{ -ht} Cosh ( t \sqrt{x}) ##?

 

[Steve4Physics]

How to write :
##Eq= e^{t ( -h \pm \sqrt{ x} )}##

I presume that represents 2 different 'equations':
##f(t,h,x)= e^{t ( -h + \sqrt{ x} )}## and
##g(t,h,x)= e^{t ( -h - \sqrt{ x} )}##

##Cosh (x) = e^x + e^{-x} /2 ##

You are missing brackets and should use a lower case c for ##\cosh##.

The eqution can be written as:
##Eq= e^{t( -h + \sqrt{ x} )} + e^{t( -h -\sqrt{ x} )}##

Looks like you are trying to express the two differnt equations as a single equation. That sounds wrong to me. It's a bit like saying ##x = 1 \pm \sqrt 2## and then considering the value of ##(1+\sqrt 2) + (1 -\sqrt 2)## (which is ##2##). It doesn't work.

 

[PeroK]

Can you please write the formula?

It's fairly obvious. I thought the question was to relate that to ##\cosh x##, which I don't think can be simply done.

 

[Chestermiller]

$$2e^{-ht}=\cosh{ht}-\sinh{ht}$$

 

[haruspex]

Homework Statement: How to write this expression in terms of a Hyperbolic function
Relevant Equations: How to write :

##
Eq= e^{t ( -h \pm \sqrt{ x} )}
##

I terms of ##Cosh (x) = e^x + e^{-x} /2 ##

Is this the question as given to you, or does it represent where you got to in answering some other question? If the latter, please state the original question.