If `cosA=4/3` and `cosB=12/13`, then find the values of `cos(A+B)` and `sin(A-B)`, where `(3pi)/(2)` lt A, B lt `2pi`.

Explanation

To solve the problem, we need to find the values of \( \cos(A+B) \) and \( \sin(A-B) \) given that \( \cos A = \frac{4}{5} \) and \( \cos B = \frac{12}{13} \), with \( A \) and \( B \) in the fourth quadrant.

### Step 1: Find \( \sin A \) and \( \sin B \)

Since \( A \) and \( B \) are in the fourth quadrant, \( \sin A \) and \( \sin B \) will be negative. We can find \( \sin A \) and \( \sin B \) using the Pythagorean identity:

\[
\sin^2 A + \cos^2 A = 1
...