JEE Math Practice Question

Let $$\alpha ,\,\beta $$ be such that $$\pi < \alpha - \beta < 3\pi $$. If $$sin{\mkern 1mu} \alpha + \sin \beta = - {{21} \over {65}}$$ and $$\cos \alpha + \cos \beta = - {{27} \over {65}}$$ then the value of $$\cos {{\alpha - \beta } \over 2}$$ :

1. A.$${{ - 6} \over {65}}\,\,$$
2. B.$${3 \over {\sqrt {130} }}$$
3. C.$${6 \over {65}}$$
4. D.$$ - {3 \over {\sqrt {130} }}$$