2025 AHS PRELIMS P1 Q10

Given that \(\sin A\) and \(\cos B\) are in the same quadrant such that \(\sin A=\frac{3}{5}\) and \(\cos B=-\frac{5}{13}\).

Find, without using a calculator, the value of

1. \(\cos(A-B)\),[2]
2. \(\cos\frac{A}{2}\).[3]