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

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

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)`
`implies tan^(-1)((2x+3x)/(1-6x^(2)))=(pi)/(4)`
`implies(5x)/(1-6x^(2))="tan"(pi)/(4)`
`implies(5x)/(1-6x^(2))=1`
`implies6x^(2)+5x-1=0`
`implies6x^(2)+6x-x-1=0`
`implies(6x-1)(x+1)=0`
`impliesx=(1)/(6),x ne -1`
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