2022 · Q59
If tan² θ + 3 sec θ - 9 = 0, where 0 < θ < 90^°, then what is the value of 12 cot² θ + 3 csc θ?
Elementary MathematicsTrigonometry
- A(√3 + 1)²
- B(√3 + 2)²
- C(2√3 + 1)²
- D(3√3 + 1)²
Explanation
tan²θ+3secθ-9 = 0 becomes sec²θ+3secθ-10 = 0, giving secθ = 2 (θ = 60°). Then 12cot²60°+3csc60° = 4+2√3 = (√3+1)². Hence the keyed option is A.