If 5 sin θ - 4 cosθ = 0, 0o < θ < 90o, then the value of $\frac{5sinθ+2cosθ}{5sinθ+3cosθ}$ is :

$\frac{4}{7}$ $\frac{6}{7}$ $\frac{2}{7}$ $\frac{3}{7}$

$\frac{6}{7}$

5 sin θ - 4 cosθ = 0 tan θ = \(\frac{4}{5}\)  P = 4 & B = 5 Now , $\frac{5sinθ+2cosθ}{5sinθ+3cosθ}$ = \(\frac{5 × P/H + 2× B /H  }{5× P/H + 3× B /H}\) = \(\frac{5 × 4 + 2× 5  }{5×4 + 3× 5}\)  = \(\frac{30  }{35}\)  = \(\frac{6  }{7}\)