AIEEE 2004 | Trigonometric Ratio and Identites Question 69 | Mathematics

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 $$\cos {{\alpha - \beta } \over 2}$$ :

$${{ - 6} \over {65}}\,\,$$

$${3 \over {\sqrt {130} }}$$

$${6 \over {65}}$$

$$ - {3 \over {\sqrt {130} }}$$

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