Consider the following values of x :
1. 8
2. -4
3. `(1)/(6)`
4. `-(1)/(4)`
Which of the above values of x is/are the solutions of the equation `tan^(-1) (2x)+ tan^(-1) (3x) =(pi)/(4)`.

Options

A. 3 only
B. 2 and 3 only
C. 1 and 4 only
D. 4 only

Answer

A

Explanation

`tan^(-1)((2x+3x)/(1-2x.3x))=(pi)/(4)`
`tan^(-1)(5x)/(1-6x^(2))=(pi)/(4)`
`(5x)/(1-6x^(2))=1`
`1-6x^(2)=5x`
`6x^(2)+5x - 1 = 0`
`(6x - 1)(x + 1) = 0`
`rArr x = (1)/(6), -1`
`rArr x = (1)/(6)`
Here x = -1 rejected.