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Let alpha,beta be such that pi lt alpha-...

Let `alpha,beta` be such that `pi lt alpha-beta lt3 pi`. If `sin alpha+ sin beta=(-21)/65` and `cos alpha+ cos beta=(-27)/65`, then the value of `cos((alpha-beta)/2)` is

A

`-3/(sqrt130)`

B

`3/(sqrt130)`

C

`6/65`

D

`- 6/65`

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The correct Answer is:
A
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