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The root of the equation tan^(-1)((x-1)/...

The root of the equation `tan^(-1)((x-1)/(x+1))+tan^(-1)((2x-1)/(2x+1))=tan^(-1)((23)/(36))` is

A

`(3)/(8)`

B

`-(1)/(2)`

C

`(3)/(4)`

D

`(4)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`tan^(-1)[((x-1)/(x+1)+(2x-1)/(2x+1))/(1-((x-1)/(x+1))((2x-1)/(2x+1)))]=tan^(-1)((23)/(36))`
`rArr(4x^(2)-2)/(6x)=(23)/(36)rArr(2x^(2)-1)/(3x)=(23)/(36)`
`rArr(2x^(2)-1)/(x)=(23)/(12)`
`rArr24x^(2)-12-23x=0`
`(3x-4)(8x+3)=0`
`rArrx=(4)/(3),-(3)/(8)`
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