Solve `tan^(-1) x + cot^(-1) (-|x|) = 2 tan^(-1) 6x`

Options

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

Answer

C

Explanation

When x lt 0, wwe have `tan^(-1)(6x)=(pi)/(4)`
`rArr x =(1)/(6)`, which is not possible
When `x ge 0`, we have `(pi)/(4)=tan^(-1)(6x)-tan^(-1)(x)`
`rArr (6x-x)/(1+6x^(2))=1`
`rArr x=(1)/(2),(1)/(3)`