A) \[\left[ -\frac{1}{2},\frac{1}{2} \right]\]
B) \[\left[ \frac{1}{2},1 \right]\]
C) \[\left[ -1,-\frac{1}{2} \right]\]
D) \[[-1,1]\]
Correct Answer: D
Solution :
[d] Let \[{{\sin }^{-1}}x=\theta \Rightarrow x=\sin \theta \] \[{{\sin }^{-1}}(3sin\theta -4si{{n}^{3}}\theta )=si{{n}^{-1}}\sin 3\theta \] \[=3\theta =3{{\sin }^{-1}}x\] Equation \[{{\sin }^{-1}}(3x-4{{x}^{3}})=3si{{n}^{-1}}x\]is true for all values of x lying the interval [-1, 1].
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