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Question
Solve `tan^-1 2x + tan^-1 3x = pi/4`
Solution
Given tan-1 (2x) + tan-1 (3x) = `pi/4`
`tan^-1 [(2x + 3x)/(1 - (2x)(3x))] = pi/4`
`tan^-1 [(5x)/(1 - 6x^2)] = pi/4`
`(5x)/(1 - 6x^2) = tan pi/4`
`(5x)/(1 - 6x^2)` = 1
⇒ 5x = 1(1 – 6x2)
⇒ 6x2 + 5x – 1 = 0
⇒ (x + 1) (6x – 1) = 0
⇒ x + 1 = 0 (or) 6x – 1 = 0
⇒ x = -1 (or) x = `1/6`
x = -1 is rejected. It doesn’t satisfies the question.
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