  For the radial and one-dimensional Schr\"{o}dinger operator $H$ with growing
potential $q(x)$ we outline a method of obtaining the trace identities - an
asymptotic expansion of the Fredholm determinant $\mathrm{det}_{F}(H-\lambda
I)$ as $\lambda\to-\infty$. As an illustrating example, we consider
Schr\"{o}dinger operator with the potential $q(x)=2\cosh 2x$, associated with
the modified Mathieu equation.
