2022 · Q51
If tan θ = (√(q²-p²))/(p); 0 < θ < 90°, then what is sec θ + cos θ + 2 equal to?
Elementary MathematicsTrigonometry
- A(p²+q²)/(pq)
- B(p+q)²/(pq)
- C(p+q)²/(2pq)
- D(p-q)²/(pq)
Explanation
secθ = √(1+tan²θ) = √((p²+q²−p²)/p²) = q/p (θ acute). Then secθ+cosθ+2 = q/p+p/q+2 = (p+q)²/(pq). The keyed option is B.