2026 · Q100
For the next two (02) items that follow:
p = sinθ/(1 + cosθ + sinθ) and q = (1 + sinθ)/(1 + sinθ − cosθ).
100. What is (p + 1/q)(q + 1/p) equal to?
Elementary MathematicsTrigonometry
- A1/2
- B17/4
- C9/2
- D21/4
Explanation
(p+1/q)(q+1/p)=pq+1/(pq)+2. From the previous item pq=1/2, so this equals 1/2+2+2=9/2, option C. Since pq is fixed at 1/2, the whole expression is constant regardless of θ.