imo class 12 inverse trigonometric functions

The range of f(x) = sin⁻¹x + cos⁻¹x is:

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The range of f(x) = sin⁻¹x + cos⁻¹x is:

  • A. [−π/2, π/2]
  • B. [0, π]
  • C. {π/2}
  • D. [−π, π]

Answer: C) {π/2}

Explanation: For any x ∈ [−1, 1], sin⁻¹x + cos⁻¹x = π/2. Since the domain of both functions is [−1, 1], the range of their sum is the single value π/2, i.e., {π/2}.

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