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

Question

$\begin{array}{1 1}(a)\;\large\frac{b^2-a^2}{b^2+a^2}&(b)\;\large\frac{b^2+a^2}{b^2+a^2}\\(c)\;\large\frac{a^2-b^2}{b^2+a^2}&(d)\;None\;of\;these\end{array}$