2026 · Q92
For the next two (02) items that follow:
Let 12(tanθ + cotθ) = 25, where 45° < θ < 90°.
92. What is a value of (cosecθ + secθ)?
Elementary MathematicsTrigonometry
- A4
- B35/12
- C25/12
- D2
Explanation
cosecθ+secθ=(sinθ+cosθ)/(sinθcosθ). From the previous item sinθcosθ=12/25 and sinθ+cosθ=√(1/25+48/25)=7/5, so the value is (7/5)/(12/25)=35/12, option B. Using (sinθ−cosθ)²=1/25 from the previous item is what makes the numerator tractable.