# Tagged Questions

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### How does $\frac{1}{2}\cosh(2x) -1 = \sinh^2(x)$?

Using hyperbolic trigonometric function identities is there a way to prove the following equation? $$\frac{1}{2} (\cosh(2x)-1) = \sinh^2(x)$$
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### Calculate cosh(x) given sinh(x)

Given the value of sinh(x) for example sinh(x) = 3/2 How can I calculate the value of cosh(x) ?
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### Showing that $\sinh(\mathrm{e}^z)$ is entire

I am attempting to show that $\sinh(\mathrm{e}^z)$, where $z$ is a complex number, is entire. The instructions of the problem tell me to write the real component of this function as a function of $x$ ...
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### Rewriting a hyperbolic equation in standard form

$9x^2-4y^2-72x$ = 0 How would that be done? So far, I got up to $\frac{9(x^2-8x)}1-\frac{4(y-0)^2}1=0$
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### Hyperbolic Functions

Hey everyone, I need help with questions on hyperbolic functions. I was able to do part (a). I proved for $\sinh(3y)$ by doing this: \begin{align*} \sinh(3y) &= \sinh(2y +y)\\ &= ...
### Inverse Laplace Transform involving $\cosh$.
While doing an assignment on solving a PDE I stumbled into the following inverse Laplace transform question (involving $\cosh$? I can't believe it). Mathematica gives no solution and I have no idea ...