2023 · Q47
If sin θ = (12)/(13) then what is the value of (tan θ + sec θ)² (csc θ - cot θ)⁻² 0 < θ < (π)/(2)
Elementary MathematicsTrigonometry
- A121/4
- B169/9
- C196/9
- D225/4
Explanation
sinθ = 12/13 with θ acute gives cosθ = 5/13. Then tanθ + secθ = 12/5 + 13/5 = 5, and cscθ − cotθ = 13/12 − 5/12 = 2/3. The expression equals 5² × (2/3)^{−2} = 25 × 9/4 = 225/4 (D).