If tanθ = \(\frac{5}{4}\), then what is the value of \(\frac{5sinθ + 4cosθ}{5sinθ - 4cosθ}\)?

\(\frac{16}{25}\)   \(\frac{41}{9}\) \(\frac{41}{25}\) \(\frac{23}{9}\)

\(\frac{41}{9}\)

tanθ = \(\frac{5}{4}\) ⇒ \(\frac{5 sinθ + 4 cosθ}{5 sinθ - 4 cosθ}\) = \(\frac{cosθ (5 tanθ + 4)}{cosθ (5 tanθ + 4)}\) = \(\frac{5 tanθ + 4}{5 tanθ - 4}\) = \(\frac{5 × \frac{5}{4} + 4}{5 × \frac{5}{4} - 4}\) = \(\frac{\frac{25}{4} + 4}{\frac{25}{4} - 4}\) = \(\frac{41}{9}\)