Question

tan⁻¹(x+1)+tan⁻¹(x-1)=tan⁻¹8/31,Solve it.

Answer 1

Solution :

Given, tan⁻¹(x + 1) + tan⁻¹(x - 1) = tan⁻¹(8/31)

⇒ tan⁻¹[{(x + 1) + (x - 1)}/{1 - (x + 1)(x - 1)}] = tan⁻¹(8/31)

⇒ {x + 1 + x - 1}/{1 - (x² - 1)} = 8/31

⇒ 2x/(1 - x² + 1) = 8/31

⇒ 2x/(2 - x²) = 8/31

⇒ 31 * x = 4 (2 - x²)

⇒ 31x = 8 - 4x²

⇒ 4x² + 31x - 8 = 0

⇒ 4x² + 32x - x - 8 = 0

⇒ 4x (x + 8) - 1 (x + 8) = 0

⇒ (x + 8) (4x - 1) = 0

∴ either x + 8 = 0 or, 4x - 1 = 0

⇒ x = - 8 or, x = 1/4 [ but x > 0 ]

∴ the required solution is x = 1/4.

Answer 2

Answer:

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