I'm trying to simplify the following equation:
$y = \dfrac{1-2\exp(-x)\cos(x)+\exp(-2x)}{1+2\exp(-x)\sin(x)-\exp(-2x)}$
I suspect that a simpler form using complex exponents exists, but I can't find it.
For context, this equation describes the effective conductivity due to the skin effect of a flat conductor as a function of its thickness. I just removed some scale factors for simplicity. The underlying differential equation gives rise to expressions of the form $\exp(\pm(1+i)x)$, which is where the $\sin(x)$ and $\cos(x)$ came from.