If 4 tan θ = 3, then $\Big(\dfrac{4\sin\theta - 3\cos\theta}{4\sin\theta + 3\cos\theta}\Big)$ = ?

1. 0

2. $\Big(\dfrac{1}{3}\Big)$

3. $\Big(\dfrac{2}{3}\Big)$

4. $\Big(\dfrac{3}{4}\Big)$

tan θ = $\dfrac{3}{4}$

Then,

sin θ = $\dfrac{3}{5}$, cos θ = $\dfrac{4}{5}$

Substitute,

$\Rightarrow \dfrac{4\Big(\dfrac{3}{5}\Big) - 3\Big(\dfrac{4}{5}\Big)}{4\Big(\dfrac{3}{5}\Big) + 3\Big(\dfrac{4}{5}\Big)} \\[1em] \Rightarrow \dfrac{\Big(\dfrac{12}{5}\Big) - \Big(\dfrac{12}{5}\Big)}{\Big(\dfrac{12}{5}\Big) + \Big(\dfrac{12}{5}\Big)} \\[1em] \Rightarrow \dfrac{0}{\dfrac{24}{5}} \\[1em] \Rightarrow 0.$

Hence, option 1 is the correct option.