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Solve tan^(-1)2x+tan^(-1)3x=pi/4....

Solve `tan^(-1)2x+tan^(-1)3x=pi/4`.

A

`1/2` or `-2`

B

`1/3` or `-3`

C

`1/4` or `-2`

D

`1/6` or `-1`

Text Solution

Verified by Experts

The correct Answer is:
D
`tan^(-1)3x+tan^(-1)3=tan^(-1)2x=pi/4 rArr tan^(-1)((3x+2x)/(1-6x^(2))=pi/4`.
`therefore (5x)/(1-6x^(2))=tanpi/4 =1 rArr 6x^(2)+5x-1=0`
`rArr (x+1)(6x-1)=0`.
`rArr x=-1` or `x=1/6`.
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