If sin⁻¹(1−x) − 2 sin⁻¹x = π/2, then x equals:
If sin⁻¹(1−x) − 2 sin⁻¹x = π/2, then x equals:
- A. 0
- B. 1/2
- C. 0 or 1/2
- D. −1/2
Answer: A) 0
Explanation: sin⁻¹(1−x) = π/2 + 2 sin⁻¹x. Taking sine: 1−x = cos(2 sin⁻¹x) = 1 − 2x², so 2x² − x = 0 and x = 0 or 1/2. Substituting back, only x = 0 satisfies the equation (x = 1/2 gives −π/6), so x = 0.
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