The simplified form of cos⁻¹(1 − 2x²) for x in [0, 1] is:
The simplified form of cos⁻¹(1 − 2x²) for x in [0, 1] is:
- A. 2 cos⁻¹(x)
- B. 2 sin⁻¹(x)
- C. sin⁻¹(2x)
- D. cos⁻¹(x)
Answer: B) 2 sin⁻¹(x)
Explanation: Put x = sin θ. Then 1 − 2sin² θ = cos 2θ. Hence cos⁻¹(cos 2θ) = 2θ = 2 sin⁻¹(x).
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