2022 · Q52
If 11 sin θ + 60 cos θ = 61; 0 < θ < 90°, then what is the value of √(660(tanθ +cotθ ))?
Elementary MathematicsTrigonometry
- A61
- B61√2
- C122
- D122√2
Explanation
Since √(11²+60²) = 61, equality in Cauchy–Schwarz forces sinθ = 11/61, cosθ = 60/61. Then tanθ+cotθ = 1/(sinθcosθ), so 660(tanθ+cotθ) = 660·61²/(11·60) = 3721 = 61², whose square root is 61. The keyed option is A.