Question:

Step 1: Identify the given information and target expression. We are given that $\tan \alpha = 2$, and we need to find the value of: $$\frac{\sin \alpha + \cos \alpha}{3 \sin \alpha - 2 \cos \alpha}$$ Step 2: Divide both numerator and denominator by $\cos \alpha$. To simplify the expression, we divide both the numerator and denominator by $\cos \alpha$: $$\frac{\sin \alpha + \cos \alpha}{3 \sin \alpha - 2 \cos \alpha} = \frac{\frac{\sin \alpha}{\cos \alpha} + \frac{\cos \alpha}{\cos \alpha}}{3 \cdot \frac{\sin \alpha}{\cos \alpha} - 2 \cdot \frac{\cos \alpha}{\cos \alpha}}$$ Step 3: Convert to tangent form. Using the identity $\frac{\sin \alpha}{\cos \alpha} = \tan \alpha$ and $\frac{\cos \alpha}{\cos \alpha} = 1$, the expression becomes: $$\frac{\tan \alpha + 1}{3 \tan \alpha - 2}$$ Step 4: Substitute the given value $\tan \alpha = 2$. Substituting $\tan \alpha = 2$ into the simplified expression: $$\frac{2 + 1}{3(2) - 2} = \frac{3}{6 - 2} = \frac{3}{4}$$ Step 5: State the final answer. The value of $\frac{\sin \alpha + \cos \alpha}{3 \sin \alpha - 2 \cos \alpha}$ is $\boxed{\frac{3}{4}}$. This corresponds to **Option 2: 3/4**.