Explanation:

- We are given that \( \sin A = \frac{4}{5} \).

- Since \( \sin^2 A + \cos^2 A = 1 \), we calculate \( \cos A \).

- \( \cos^2 A = 1 - \left(\frac{4}{5}\right)^2 = \frac{9}{25} \), hence \( \cos A = \frac{3}{5} \).

- Now, calculate \( \tan A \): \(\tan A = \frac{\sin A}{\cos A} = \frac{4/5}{3/5} = \frac{4}{3}\).

- Plug values into the expression: \( (3 - \tan A) (2 + \cos A) \).

- Substitute: \( (3 - \frac{4}{3}) (2 + \frac{3}{5}) = \left(\frac{9}{3} - \frac{4}{3}\right) \left(\frac{10}{5} + \frac{3}{5}\right) \).

- Simplifying: \( \left(\frac{5}{3}\right)(\frac{13}{5}) = \frac{65}{15} = \frac{13}{3} \).

Answer: Option 2: \(\frac{13}{3}\).