2022 · Q59
What is the minimum value of 3600 sec²θ + 121 csc²θ, where 0 < θ < (π)/(2)?
Elementary MathematicsTrigonometry
- A1320
- B2401
- C3721
- D5041
Explanation
By Cauchy–Schwarz, the minimum of a·sec²θ+b·cosec²θ is (√a+√b)² = (60+11)² = 5041. Equality holds when √a·tanθ = √b·cotθ, i.e. tan²θ = 121/3600. The keyed option is D.