2022 · Q56
If (sinθ +cosθ )/(sinθ -cosθ ) = 5, where 0 < θ < (π )/(2), θ ≠ (π )/(4), then what is the value of (2sinθ +3cosθ )/(3sinθ -2cosθ )?
Elementary MathematicsTrigonometry
- A8/5
- B2
- C12/5
- D3
Explanation
(sinθ+cosθ)/(sinθ−cosθ) = 5 gives 6cosθ = 4sinθ, so tanθ = 3/2. Dividing numerator and denominator by cosθ: (2tanθ+3)/(3tanθ−2) = 6/2.5 = 12/5. The keyed option is C.