2025 · Q47
If (1+sinθ)/cosθ = p+√(p^2+1), then what is secθ equal to?
Elementary MathematicsTrigonometry
- Ap
- B√(p^2+1)
- Cp+1
- D2p
Explanation
sec(theta)+tan(theta)=(1+sin(theta))/cos(theta)=p+sqrt(p^2+1)=u. Since sec(theta)-tan(theta)=1/u=sqrt(p^2+1)-p, adding gives 2sec(theta)=2*sqrt(p^2+1), so sec(theta)=sqrt(p^2+1). Using sec^2-tan^2=1 to get the conjugate equation is the key step.