Hello,
How can you prove that:
$\displaystyle \Gamma(x) \cdot \Gamma(1-x) = \dfrac{\pi}{sin(\pi x)}$ ?!
This is a well known formula: Reflection formula - Wikipedia, the free encyclopedia
I don't plan to re-invent the wheel. You will find it proved in many textbooks that deal with this sort of stuff (go to your your institute's library) and I have no doubt a Google search will turn up many websites that prove it.