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If sin x + sin y = (sqrt(3) + 1)/(2) and...

If `sin x + sin y = (sqrt(3) + 1)/(2)` and `cos x + cos y = (sqrt(3) - 1)/(2)`, then `tan^(2)((x-y)/(2)) + tan^(2)((x+y)/(2)) =`

A

`8 + 4sqrt(3)`

B

`6 + 4sqrt(3)`

C

`3 + sqrt(3)`

D

`12 + 6sqrt(3)`

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The correct Answer is:
A
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