If cos⁻¹(x/2) + cos⁻¹(y/3) = θ, then 9x² − 12xy cos θ + 4y² is equal to:
If cos⁻¹(x/2) + cos⁻¹(y/3) = θ, then 9x² − 12xy cos θ + 4y² is equal to:
- A. 36 sin² θ
- B. 36 cos² θ
- C. 18 sin² θ
- D. 18 cos² θ
Answer: A) 36 sin² θ
Explanation: Applying cos(A+B) formula gives (xy/6) − √((1−x²/4)(1−y²/9)) = cos θ. Rearranging and squaring gives 9x² − 12xy cos θ + 4y² = 36 sin² θ.
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