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) ?
Use the identity $\cosh^2x-\sinh^2x \equiv 1$. If $\sinh x = \frac{3}{2}$ then
$$\cosh^2x - \left(\frac{3}{2}\right)^{\! 2} = 1$$
$$\cosh^2x - \frac{9}{4} = 1$$
$$\cosh^2x = \frac{13}{4}$$
It follows that $\cosh x = \pm\frac{1}{2}\sqrt{13}$. Since $\cosh x \ge 1$ for all $x \in \mathbb{R}$ we have $\cosh x = \frac{1}{2}\sqrt{13}$.
Do you want to say that $cosh^2x-sinh^2x=1$? Yes that is correct because of this:
$1/4[e^{2x}+2+e^{-2x}-e^{2x}+2-e^{-2x}]= 1/4 \times 4=1$