If y = (sin⁻¹ x)², then (1 − x²)y₂ − xy₁ equals:
If y = (sin⁻¹ x)², then (1 − x²)y₂ − xy₁ equals:
- A. 2
- B. 0
- C. y
- D. 2y
Answer: A) 2
Explanation: y₁ = 2 sin⁻¹ x / √(1−x²). √(1−x²) y₁ = 2 sin⁻¹ x. Squaring gives (1−x²)y₁² = 4y. Differentiating: −2x y₁² + (1−x²)2y₁y₂ = 4y₁. Cancel 2y₁: −x y₁ + (1−x²)y₂ = 2. Thus (1−x²)y₂ − xy₁ = 2.
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