Show that the value of $\sin 105{}^\circ$ can be expressed as $\frac{1}{4}(p+q)$, where&nbs

Question

Show that the value of $\sin 105{}^\circ$ can be expressed as $\frac{1}{4}(p+q)$, where $p$ and $q$ are constants.[3] Given that $\frac{\cos(A+B)}{\cos(A-B)} = \frac{2}{7}$ and $\sin A \sin B \neq 0$, find the exact value of $\cot A \cot B$.[3] Given that $B$ is a reflex angle and $\cot B = 3$, find the exact value of $\cos2B$[2]

Accepted Answer

(a)$p=\sqrt 2, q=\sqrt 6$ (b)$\frac{9}{5}$ (c)$\frac{4}{5}$

2025 SCGS PRELIMS P1 Q9

2025 SCGS PRELIMS P1 Q9