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 different 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.