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

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

A

Is an empty set

B

Contains two elements

C

Contains more than two elements

D

Is a singleton

Text Solution

Verified by Experts

The correct Answer is:
D
`tan^(-1)2x+tan^(-1)3x=(pi)/(4)rArr tan^(-1) (2x+2x)/(1-6x^2)=(pi)/(4) rArr (2x+3x)/(1-6x^2)=16x^2+5x-1=0`
`(x+1)(6x-1)=0`
`x=-1`(Ruled out) `(because x ge 0)=(1)/(6)` .
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