2025 PHS PRELIMS P1 Q2

It is given that \(\cos A=\frac{1}{2}\) and \(\sin B=-\frac{1}{\sqrt{2}}\) where \(0^\circ<A<90^\circ\) and \(180^\circ<B<270^\circ\).

Find, without using a calculator, the exact value of \(\cos(A-B)\), leaving your answer in the form \(p\sqrt{2}+q\sqrt{6}\), where \(p\) and \(q\) are real numbers.[4]