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Solve tan^(-1) x + cot^(-1) (-|x|) = 2 t...

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

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If `x gt0`
`tan^(-1) x + cot^(-1) (-x) = 2 tan^(-1) 6x`
`rArrr tan^(-1) x + pi - cot^(-1) x = 2 tan^(-1) 6x`
`rArr (pi)/(2) + 2 tan^(-1) x = 2 tan^(-1) 6x`
`rArr tan^(-1) 6x - tan^(-1) x = (pi)/(4)`
`rArr tan^(-1).(6x - x)/(1 + 6x^(2)) = (pi)/(4)`
`rArr (5x)/(1 + 6x^(2)) =1`
`rArr 6x^(2) -5x + 1 = 0`
`rArr x = (1)/(2), (1)/(3)`
If `x lt 0`
`tan^(-1) x + cot^(-1) x = 2 tan^(-1) 6x`
`rArr tan^(-1) 6x = (pi)/(4)`, This is not possible as `x lt 0`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
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