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The range of function f(x)=cot^(-1)x+sec...

The range of function `f(x)=cot^(-1)x+sec^(-1)x+ cosec^(-1)x` is
(A)`[(pi)/(2), pi)uu(pi, (3 pi)/(2)]`
(B)`((pi)/(2), (3 pi)/(4)] uu [(5 pi)/(4), (3 pi)/(2))`
(C)`((pi)/(2), pi)uu(pi ,(3 pi)/(2))`
(D)`((pi)/(2), (3 pi)/(2))`

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