If −$$12$$≤x≤$$12$$, then $$sin$$−$$1$$⁡$$3x$$−$$4x3equals$$

Correct option is 13sin−1⁡x

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If $- \frac{1}{2} \leq x \leq \frac{1}{2},$ then $\sin^{- 1} (3 x - 4 x^{3})$ equals

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3sin−1⁡x

π−3sin−1⁡x

−π−3sin−1⁡x

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detailed solution

Correct option is A

Let sin−1⁡x=θ. Then, x=sin⁡θAlso, −12≤x≤12⇒−12≤sin⁡θ≤12⇒−π6≤θ≤π6.Now, sin−1⁡3x−4x3=sin−1⁡(sin⁡3θ)⇒ sin−1⁡3x−4x3=3θ∵−π6≤0≤π6⇒−π2≤3θ≤π2⇒ sin−1⁡3x−4x3=3sin−1⁡x

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If −12≤x≤12, then sin−1⁡3x−4x3equals

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If $- \frac{1}{2} \leq x \leq \frac{1}{2},$ then $\sin^{- 1} (3 x - 4 x^{3})$ equals