Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsIdentities, eqations and inequations involving ITFMedium2 min

MathematicsMediumsingle choice

If $0 < x < 1$ , the number of solutions of the equation $tan^{- 1} (x - 1) + tan^{- 1} x + tan^{- 1} (x + 1) = tan^{- 1} 3 x$ is

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Answer:

Solution:

The given equation can be written as

$tan^{- 1} (x - 1) + tan^{- 1} (x + 1) = tan^{- 1} 3 x - tan^{- 1} x \Rightarrow \frac{2 x}{2 - x ^{2}} = \frac{2 x}{1 + 3 x ^{2}} \Rightarrow x + 3 x^{3} = 2 x - x^{3} \Rightarrow 4 x^{3} - x = 0 \Rightarrow x (4 x^{2} - 1) = 0 \Rightarrow x = 0, x = \pm \frac{1}{2} . Thus x = \frac{1}{2}$

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:Identities, eqations and inequations involving ITF

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