2025 · Q50
If sinθ+cosθ = p and secθ+cosecθ = q, then what is tanθ+cotθ equal to?
Elementary MathematicsTrigonometry
- Ap/q
- Bq/p
- C2p/q
- D2q/p
Explanation
tan(theta)+cot(theta)=(sin^2(theta)+cos^2(theta))/(sin(theta)cos(theta))=1/(sin(theta)cos(theta)). From Q49, q=p/(sin(theta)cos(theta)), so 1/(sin(theta)cos(theta))=q/p. Hence tan(theta)+cot(theta)=q/p.