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Let alpha = tan^-1 (1/2)+tan^-1(1/3),bet...

Let `alpha = tan^-1 (1/2)+tan^-1(1/3)`,`beta=cos^-1(2/3)+cos^-1(sqrt5/3)`, `gamma=sin^-1(sin((2pi)/3))+1/2cos^-1(cos((2pi)/3))`
then`cosalpha+cosbeta+cosgamma` is equal to
(A) `(sqrt(2)-1)/2` (B) `(sqrt(2)+1)/2` (C) `(sqrt(2)+sqrt(3))/2` (D) `((sqrt(3)-sqrt(2))/2)`

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