If 5 sin θ - 4 cosθ = 0, 0o < θ < 90o, then the value of $\frac{5sinθ+2cosθ}{5sinθ+3cosθ}$ is :
Answer & explanation
Correct answer: option 2
5 sin θ - 4 cosθ = 0
tan θ = \(\frac{4}{5}\)
P = 4 & B = 5
Now , $\frac{5sinθ+2cosθ}{5sinθ+3cosθ}$
= \(\frac{5 × P/H + 2× B /H }{5× P/H + 3× B /H}\)
= \(\frac{5 × 4 + 2× 5 }{5×4 + 3× 5}\)
= \(\frac{30 }{35}\)
= \(\frac{6 }{7}\)