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If cos A + cos B =a, and sin A + sin B =...

If `cos A + cos B =a`, and `sin A + sin B = b` where `a,b cancel(=)0`, then `sin ( A+B)` is equal to

A

`(a^(2)+b^(2))/(2)`

B

`(a^(2)-b^(2)+2)/(2)`

C

`(a^(2)+b^(2)-2)/(2)`

D

None of these

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The correct Answer is:
C
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