If $\sin\alpha+\sin\beta=\alpha$ and $\cos\alpha+\cos\beta=b$ then $\sin(\alpha+\beta)$ is equal to

Question

$(a)\;\large\frac{2ab}{a^2-b^2}\qquad$$(b)\;\large\frac{ab}{a^2-b^2}\qquad$$(c)\;\large\frac{ab}{a^2+b^2}$$\qquad(d)\;\large\frac{2ab}{a^2+b^2}$