2026 · Q97
For the next two (02) items that follow:
p + q·cotθ = 3·cosecθ and q − p·cotθ = 2·cosecθ.
97. What is p² + q² equal to?
Elementary MathematicsTrigonometry
- A5
- B7
- C10
- D13
Explanation
Squaring and adding the two equations: (p+q·cotθ)²+(q−p·cotθ)²=(p²+q²)(1+cot²θ)=(p²+q²)cosec²θ. The right side is 13cosec²θ, so p²+q²=13, option D. The cross terms ±2pq·cotθ cancel — missing that is the trap.