Beta Function of Half with Half/Proof 1

Proof
By definition of the Beta function:


 * $\displaystyle \Beta \left({x, y}\right) := 2 \int_0^{\pi / 2} \left({\sin \theta}\right)^{2x - 1} \left({\cos \theta}\right)^{2y - 1} \rd \theta$

Thus: