The simplified form of sin⁻¹(2x√(1−x²)) for x in [−1/√2, 1/√2] is:
The simplified form of sin⁻¹(2x√(1−x²)) for x in [−1/√2, 1/√2] is:
- A. 2 cos⁻¹(x)
- B. sin⁻¹(x)
- C. 2 sin⁻¹(x)
- D. cos⁻¹(2x)
Answer: C) 2 sin⁻¹(x)
Explanation: Put x = sin θ. Then 2sin θ cos θ = sin(2θ). Therefore sin⁻¹(sin 2θ) = 2θ = 2 sin⁻¹(x).
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