Solve for x: ^ -1 (x + 1) + ^ -1 (x - 1) = ^ -1 8 31 - Vidyadip

Question

$\text{Solve for x:}$
$\tan^{-1}(\text{x + 1)} + \tan^{-1}(\text{x - 1)} = \tan^{-1}\frac{8}{31}$

✓

Answer

$\tan^{-1}\Bigg(\frac{\text{x + 1 + x - 1}}{1 - {\text(\text{x})(\text{x} - 1)}}\Bigg) = \tan^{-1}\bigg(\frac{8}{31}\bigg)$
$\Rightarrow \frac{\text{2x}}{\text{2 - x}^{2}} = \frac{8}{31} \therefore\text{4x}^{2} + \text{31x - 8 = 0}$
$\therefore \text{x} = \frac{1}{4}, \text{-8 (Rejected)}$

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