2025 · Q49
If sinθ+cosθ = p and secθ+cosecθ = q, where p≠1, then which one of the following is correct?
Elementary MathematicsTrigonometry
- Ap=q(p^2-1)
- B2p=q(p^2-1)
- Cq=p^2-1
- D2q=p(p^2-1)
Explanation
q=sec(theta)+cosec(theta)=(sin(theta)+cos(theta))/(sin(theta)cos(theta))=p/(sin(theta)cos(theta)). Since sin(theta)cos(theta)=((sin(theta)+cos(theta))^2-1)/2=(p^2-1)/2, q=2p/(p^2-1), i.e. 2p=q(p^2-1). The p=/=1 condition keeps the denominator nonzero.