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For any yinR, let cot^(-1)(y)in(0,\pi ) and
tan^(-1)(y)in(-(\pi )/(2),(\pi )/(2)) Then the sum of all the solutions of
the equation tan^(-1)((6y)/(9-y^(2)))+cot^(-1)((9-y^(2))/(6y))=(2\pi )/(3) for
0<|y|<3, is equal to:
(A) 2\sqrt(3)-3
(B) 3-2\sqrt(3)
(C) 4\sqrt(3)-6
(D) 6-4\sqrt(3)

Sagot :

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