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If tan^(-1)(2x)+tan^(-1)(3x)=(pi)/(4), t...

If `tan^(-1)(2x)+tan^(-1)(3x)=(pi)/(4)`, then find the value of x.

A

`-1`

B

`(1)/(3)`

C

`(1)/(6)`

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`tan^(-1)2x+tan^(-1) 3x=(pi)/(4)`
`rArr tan^(-1) ((2x+3x)/(1-6x^(2)))=(pi)/(2)`
`rArr (5x)/(1-6x^(2))=tan. (pi)/(4)`
`rArr (5x)/(1-6x^(2))=1`
`rArr6x^(2)+5x-1=0`
`rArr 6x^(2)+6x-x-1=0`
`rArr (6x-1)(x+1)=0`
`rArrx=(1)/(6), x != -1`
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