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tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3))is equ...

`tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3))`is equal to(A) `pi` (B) `-pi/2` (C) 0 (D) `2sqrt(3)`

A

`pi`

B

`-(pi)/(2)`

C

`0`

D

`2sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
`tan^(-1)""sqrt(3)-cot^(-1)""(-sqrt(3))`
`=tan^(-1)""sqrt(3)-(pi-cot^(-1)""sqrt(3))`
`=tan^(-1)""sqrt(3)-pi+ cot^(-1)""sqrt(3)`
`=(tan^(-1)""sqrt(3)+cot^(-1)""sqrt(3))-pi`
`=(pi)/(2)-pi=-(pi)/(2)`
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