If `s in A=(12)/(13)a n dsinB=4/5,\ w h e r e\ pi/2

Explanation

To solve the problem, we need to find \( \cos(A + B) \) given that \( \sin A = \frac{12}{13} \) and \( \sin B = \frac{4}{5} \), with the constraints \( \frac{\pi}{2} < A < \pi \) and \( 0 < B < \frac{\pi}{2} \).

### Step 1: Find \( \cos A \)

Using the identity \( \sin^2 A + \cos^2 A = 1 \), we can express \( \cos A \) as follows:

\[
\cos A = -\sqrt{1 - \sin^2 A}
...