Solve for x: ^ -1 3x + ^ -1 2x = 4 - Vidyadip

Question

$\text{Solve for x:} \tan^{-1} 3x + \tan^{-1} 2x = \frac{ \pi}{4}$

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Answer

$\tan^{-1} 3x + \tan^{-1} 2x = \frac{\pi}{4} \Rightarrow \tan^{-1}\bigg(\frac{5x}{1 - 6x^{2}}\bigg) = \frac{\pi}{4}$$\Rightarrow \frac{5x}{1 - 6x^{2}} = 1 \Rightarrow 6x^{2} + 5x - 1 = 0$
$\text{Solving to get x} = -1, \text{x} = \frac{1}{6} $
$\text{x} = -1 \text{does not satisfy the equation,} \therefore \text{x} = \frac{1}{6} \text{is the solution}$

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