The maximum value of (sin⁻¹(x))² + (cos⁻¹(x))² is:
The maximum value of (sin⁻¹(x))² + (cos⁻¹(x))² is:
- A. π²/4
- B. 5π²/4
- C. π²/2
- D. π²
Answer: B) 5π²/4
Explanation: Let a = sin⁻¹(x). Then (cos⁻¹(x))² = (π/2 − a)². The sum is 2a² − πa + π²/4. The maximum occurs at the domain boundary a = −π/2 (when x = −1), yielding 5π²/4.
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