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GUJCET · Maths · Inverse Trigonometric Functions
If \(y=3 \sin ^{-1} x+\sin ^{-1}\left(3 x-4 x^3\right)\) for all \(x \in[-1 / 2,1 / 2]\), then
- A \(-\pi \leq y \leq \pi\)
- B \(-\pi / 3 \leq y \leq \pi / 3\)
- C \(-\pi / 2 \leq y \leq \pi / 2\)
- D \(-\pi / 6 \leq y \leq \pi / 6\)
Answer & Solution
Correct Answer
(A) \(-\pi \leq y \leq \pi\)
Step-by-step Solution
Detailed explanation
\(y = 3 \sin^{-1} x + \sin^{-1}(3x - 4x^3)\) For \(x \in [-1/2, 1/2]\), \(\sin^{-1}(3x - 4x^3) = 3 \sin^{-1} x\).
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