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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))`
The value of `cos(alpha+beta+gamma)` is equal to
(A) `cos((5pi)/12)` (B) `cos ((7pi)/12)` (C) `-cos(pi/12)` (D) `-cos ((7pi)/12)`

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