2024 · Q52
If (sinθ -cosθ +1)/(sinθ +cosθ -1) = p sec θ + q tan θ, where 0 < θ < (π )/(2), then what is p + q equal to?
Elementary MathematicsTrigonometry
- A0
- B1
- C2
- D4
Explanation
Cross-multiplying (sinθ − cosθ + 1)cosθ = (1 + sinθ)(sinθ + cosθ − 1) reduces to an identity. This confirms the fraction equals secθ + tanθ. Hence p = q = 1 and p + q = 2, option (c).