Hi,

I want to show that $\displaystyle f(z) = \dfrac{e^z - 1}{\cos z + \sin z - 1}$ is bounded on some neighborhood of zero in the complex plane, for example on the unit circle. Any bound suffices, I have

$\displaystyle f(z) = \dfrac{e^z - 1}{\frac{1}{2}(e^{iz}+e^{-iz}) + \frac{1}{2i}(e^{iz}-e^{-iz}) - 1} = \dfrac{e^z - 1}{e^{iz}(\frac{1}{2} + \frac{1}{2i}) + e^{-iz}(\frac{1}{2} - \frac{1}{2i}) - 1}$

but I don't know what to do now.