The software maple 12 has calculated that:
$ \displaystyle \lim_{x\to 0}\Bigg( \frac {\cos(\pi x)}{\sin(\pi x)}\;\;-\;\frac{\pi x}{\sin^2 (\pi x)}\bigg)=0$
How can I prove this equality? I have tried to multiply $\displaystyle \frac{\pi x}{\pi x}$ and use the limit $\displaystyle\frac{\sin(\pi x)}{\pi x}\;=1$ but probably it is the wrong way.