It is given that $\cos A = \frac{1}{2}$ and $\sin B = -\frac{1}{\sqrt{2}}$, where \(0^

Question

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]

Accepted Answer

$-\frac{1}{4}\sqrt{2}-\frac{1}{4}\sqrt{6}$

2025 PHS PRELIMS P1 Q2

2025 PHS PRELIMS P1 Q2

Solution:

Solution locked