It is given that&nbsp;\(\cos A = \frac{1}{2}\) and \(\sin B = -\frac{1}{\sqrt{2}}\), where&nbsp;\(0^\circ &lt; A &lt; 90^\circ\) and \(180^\circ &lt; B &lt; 270^\circ\).
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&nbsp;\(p\) and \(q\) are real numbers.[4]

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.

2025 PHS P1 Q2

2025 PHS P1 Q2