$A$ and $B$ are acute angles such that $\sin{(A - B)} = \frac{3}{8}$ and \(\sin{A}\cos{B}

Question

$A$ and $B$ are acute angles such that $\sin{(A - B)} = \frac{3}{8}$ and $\sin{A}\cos{B} = \frac{5}{8} $. Without using a calculator, find the value of $\cos A \sin B$.[2] Express $2\sin 2\theta(\sec \theta - \tan \theta)$ as a quadratic expression in $\sin \theta$.[3] Use your answer to part (b) to find, for $0 \le \theta \le 2\pi$, the exact solutions of the equation $2\sin 2\theta(\sec \theta - \tan \theta) + 3 = 0$.[3]

Accepted Answer

(a) $\dfrac14$ (b) $4\sin\theta-4\sin^2\theta$ (c) $\theta=\dfrac{7\pi}{6}$ or $\dfrac{11\pi}{6}$

2024 FMSS PRELIMS P2 Q5

2024 FMSS PRELIMS P2 Q5

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