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$If \cos x + \cos y = 1 / 3, \sin x + \sin y = 1 / 4 then \cos (x + y) =$

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25/24

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25/7

answer is A.

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Detailed Solution

$\frac{\sin x + \sin y}{\cos x + \cos y} = \frac{3}{4} \Rightarrow \tan (\frac{x + y}{2}) = \frac{3}{4} \Rightarrow \cos (x + y) = \frac{1 - (9 / 16)}{1 + (9 / 16)} = \frac{7}{25} .$

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