Simplification of trigonometric functions with similar arguments

Question

I am looking to simplify the following: $$\frac{\sin\left(\frac{x+y}{2}\right)}{\sin(x+y)}$$ I have tried series expansion but I am unable to reconcile this as a single argument in terms of some trigonometric function. Hopefully one of you guys has a bright idea.

Answer 1

Use that $$\sin(x+y)=2\sin\left(\frac{x+y}{2}\right)\cos\left(\frac{x+y}{2}\right)$$