2026 · Q91
For the next two (02) items that follow:
Let 12(tanθ + cotθ) = 25, where 45° < θ < 90°.
91. What is a value of (sinθ − cosθ)?
Elementary MathematicsTrigonometry
- A−1/5
- B−2/5
- C1/5
- D2/5
Explanation
tanθ+cotθ=1/(sinθcosθ)=25/12, so sinθcosθ=12/25. Then (sinθ−cosθ)²=1−24/25=1/25; since 45°<θ<90°, sinθ>cosθ and the value is +1/5, option C. Ignoring the range gives the distractor −1/5.