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

$\frac{6}{7}$

5 sin θ - 4 cosθ = 0

tan θ = \(\frac{4}{5}\) 

P = 4 & B = 5

Now , $\frac{5sinθ+2cosθ}{5sinθ+3cosθ}$

= \(\frac{5 × P/H + 2× B /H  }{5× P/H + 3× B /H}\)

= \(\frac{5 × 4 + 2× 5  }{5×4 + 3× 5}\) 

= \(\frac{30  }{35}\) 

= \(\frac{6  }{7}\)