If cos⁻¹x > sin⁻¹x, then x belongs to:
If cos⁻¹x > sin⁻¹x, then x belongs to:
- A. [0, 1/√2)
- B. [−1, 0)
- C. [−1, 1/√2)
- D. (1/√2, 1]
Answer: C) [−1, 1/√2)
Explanation: cos⁻¹x > sin⁻¹x → π/2 − sin⁻¹x > sin⁻¹x → π/2 > 2sin⁻¹x → sin⁻¹x < π/4 → x < 1/√2. Also x ≥ −1. So x ∈ [−1, 1/√2).
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