Parametrisation of a surface in $\mathbb{R}^3$ I am trying to parameterise $M=\bigl\{(x,y,z) \mid e^z=\frac{\cos x}{\cos y}\bigr\}\subset \mathbb{R}^3$ where $x,y \in \bigl(-\frac{\pi}{2},\frac{\pi}{2}\bigr)$ in $(u,v)$ i.e $2$ variables but without any luck. Can someone see how that is supposed to be done?

Since $z=\ln\frac{\cos x}{\cos y}$, we immediately get the parametrisation
$$\left(x,y,\ln\frac{\cos x}{\cos y}\right)\qquad x,y\in(-\pi/2,\pi/2)$$
