If $${\text{tan}}\theta = \frac{4}{3}{\text{,}}$$   then the value of $$\frac{{3\sin \theta + 2\cos \theta }}{{3\sin \theta - 2\cos \theta }}$$    is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{ tan}}\theta = \frac{4}{3} \cr & \frac{{\sin \theta }}{{\cos \theta }} = \frac{4}{3} \cr & \Rightarrow \frac{{3 \times 4 + 2 \times 3}}{{3 \times 4 - 2 \times 3}} \cr & \Rightarrow \frac{{18}}{6} \cr & \Rightarrow 3 \cr} $$