2026 · Q94
For the next two (02) items that follow:
cosecθ − sinθ = p³ and secθ − cosθ = q³.
94. What is p⁴q² + p²q⁴ equal to?
Elementary MathematicsTrigonometry
- A−2
- B−1
- C0
- D1
Explanation
p⁴q²=(p³)^{4/3}(q³)^{2/3}=(cos²θ/sinθ)^{4/3}·(sin²θ/cosθ)^{2/3}=cos²θ, and similarly p²q⁴=sin²θ. Their sum is cos²θ+sin²θ=1, option D. The fractional exponents look intimidating, but each term collapses cleanly to a single squared trigonometric function.