If tan $θ = \frac{4}{3}$, then the value of $\frac{9sinθ +12 cosθ}{27cosθ-20sinθ}$ will be equal to :
Answer & explanation
Correct answer: option 1
tan θ = \(\frac{4}{3}\)
{ tan θ = \(\frac{P}{B}\) }
By using pythagoras theorem ,
P² + B² = H²
4² + 3² = H²
H = 5
Now,
\(\frac{9sinθ + 12cosθ}{27cosθ - 20sinθ}\)
= \(\frac{9 × 4 + 12 ×3}{27 ×3 - 20 ×4}\)
= \(\frac{72}{1}\)
= 72