If cos⁻¹x − cos⁻¹(y/2) = α, then 4x² − 4xy cos α + y² equals:

If cos⁻¹x − cos⁻¹(y/2) = α, then 4x² − 4xy cos α + y² equals:

• A. 4 sin²α
• B. 4 cos²α
• C. 4
• D. 2 sin²α

Answer: A) 4 sin²α

Explanation: Given α = cos⁻¹x − cos⁻¹(y/2). Take cos both sides: cos α = x·(y/2) + √(1−x²)·√(1−y²/4). Rearranging: √(1−x²)·√(4−y²) = 2cos α − xy. Squaring and simplifying gives 4x² − 4xy cos α + y² = 4(1−cos²α) = 4 sin²α.