Finding a parametrization of the solutions of $\frac{dx}{dt}=\frac{\sinh y}{\cosh y+A\cos x}$, $\frac{dy}{dt}=\frac{A\sin x}{\cosh y+A\cos x}$

Question

I am trying desperately to find a parametrization for the following:

$\frac{dx}{dt}=\frac{\sinh y}{\cosh y+A\cos x}$

$\frac{dy}{dt}=\frac{A\sin x}{\cosh y+A\cos x}$

I tried to devide the equation and do several manipulation - no actual success. Can anyone help?