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If A,B,C are the angles of a given trian...

If A,B,C are the angles of a given triangle ABC . If cosA.cosB.cosC=`(sqrt3-1)/8` and sinA.sinB.sinC=`(3+sqrt3)/8`The value of `tanA+tanB+tanC` is (A) `(3+sqrt(3)/(sqrt(3)-1))` (B) `(sqrt(3)+4/(sqrt(3)-1))` (C) `(6-sqrt(3)/(sqrt(3)-1))` (D) `(sqrt(3)+sqrt(2)/(sqrt(3)-1))`

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