If tan = 4/3 , then the value of 3 + 2 cos 3 - 2 cos is?

Answer: Option C

$$\frac{3\sin \theta +2\text{cos}\theta }{3\sin \theta -2\text{cos}\theta }$$
Divide numerator & denominator by cosθ
$$\begin{array}{rl}& =\frac{\frac{3\sin \theta }{\cos \theta }+\frac{2\cos \theta }{\cos \theta }}{\frac{3\sin \theta }{\cos \theta }-\frac{2\cos \theta }{\cos \theta }}\left[\frac{\sin \theta }{\cos \theta }=\tan \theta \right]\\ & =\frac{3\tan \theta +2}{3\tan \theta -2}\\ & \text{Put value of tan}\theta \\ & =\frac{3\times \frac{4}{3}+2}{3\times \frac{4}{3}-2}\\ & =\frac{6}{2}\\ & =3\end{array}$$