If sin⁻¹(x) > cos⁻¹(x), then x belongs to the interval:
If sin⁻¹(x) > cos⁻¹(x), then x belongs to the interval:
- A. (0, 1]
- B. [-1, 1/√2)
- C. (1/√2, 1]
- D. [-1, 0)
Answer: C) (1/√2, 1]
Explanation: sin⁻¹(x) > π/2 − sin⁻¹(x) gives 2 sin⁻¹(x) > π/2, so sin⁻¹(x) > π/4. Therefore, x > 1/√2. Since the domain is [-1, 1], x is in (1/√2, 1].
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