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प्रश्न
Solve: tan-1 (x + 1) + tan-1 (x – 1) = `tan^-1 (4/7)`
उत्तर
tan-1 (x + 1) + tan-1 (x – 1) = `tan^-1 (4/7)`
`tan^-1 (((x + 1) + (x - 1))/(1 - (x + 1)(x - 1))) = tan^-1 (4/7)`
`tan^-1 ((2x)/(1 - (x^2 - 1))) = tan^-1 (4/7)`
`tan^-1 ((2x)/(1 - x^2 + 1)) = tan^-1 (4/7)`
`tan^-1 ((2x)/(2 - x^2)) = tan^-1 (4/7)`
∴ `(2x)/(2 - x^2) = 4/7`
`(x)/(2 - x^2) = 2/7`
⇒ 7x = 2(2 – x2)
⇒ 7x = 4 – 2x2
⇒ 2x2 + 7x – 4 = 0
⇒ (x + 4) (2x – 1) = 0
⇒ x + 4 = 0 (or) 2x – 1 = 0
⇒ x = -4 (or) x = `1/2`
x = -4 is rejected, since does not satisfies the question.
∴ x = `1/2`
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