How to solve this complex limits at infinity with trig? Please consider this limit question
$$\lim_{x\rightarrow\infty}\frac{a\sin\left(\frac{a(x+1)}{2x}\right)\cdot \sin\left(\frac{a}{2}\right)}{x\cdot \sin\left(\frac{a}{2x}\right)}$$
How should I solve this? I have no idea where to start please help.

Make life easier using $x=\frac 1 y$.
So the problem reduces to 
$$\lim_{y\rightarrow 0}\left(\frac{a\, y}{\sin\left(\frac{a y}{2}\right)} \sin \left(\frac{a}{2}\right) \sin \left(\frac{a}{2}  (y+1)\right) \right)$$ and the first term looks quite familiar.
