2022 · Q60
What is √(((1+sinθ )/(cosθ ))²+((cosθ )/(1+sinθ ))²-2) equal to, where 0 < θ < (π )/(2)?
Elementary MathematicsTrigonometry
- Atan θ
- Bcot θ
- C2 tan θ
- D2 cot θ
Explanation
Put A = (1+sinθ)/cosθ; the expression is √((A−1/A)²) = |A−1/A|. Now A−1/A = [(1+sinθ)²−cos²θ]/[cosθ(1+sinθ)] = 2tanθ > 0. The keyed option is C.