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  4. Letα,β be such that π<α-β<3π.If sin α+sin β=-(21/65),cos α+ cos β=-(27/65),then the value of cos(α-β/2)is

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Q. Let$\alpha,\beta\, be such that\, \pi<\alpha-\beta<3\pi.If\,sin\,\alpha+sin\,\beta=-\frac{21}{65},cos\,\alpha+\,cos\,\beta=-\frac{27}{65},then the value of cos\frac{\alpha-\beta}{2}is$

Solution:

Correct answer is (c) $-\frac{3}{\sqrt{130}}$