If x<−$$13$$, then $$tan$$−$$1$$⁡$$3x$$−$$x31$$−$$3x2$$ equals

Correct option is 3π+3tan−1⁡x

Questions

If $x < - \frac{1}{\sqrt{3}},$ then $\tan^{- 1} (\frac{3 x - x^{3}}{1 - 3 x^{2}})$ equals

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3tan−1⁡x

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π+3tan−1⁡x

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detailed solution

Correct option is C

Let tan−1⁡x=θ. Then, x=tan⁡θAlso, x<−13⇒tan⁡θ<−13⇒−π2<θ<−π6Now, tan−1⁡3x−x31−3x2= tan−1⁡(tan⁡3θ)= tan−1⁡(tan⁡(π+30))=π+3θ=π+3tan−1⁡x

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If x<−13, then tan−1⁡3x−x31−3x2 equals

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If $x < - \frac{1}{\sqrt{3}},$ then $\tan^{- 1} (\frac{3 x - x^{3}}{1 - 3 x^{2}})$ equals