WAEC Further Mathematics 2023 Paper

$\sin \; x = \; \frac{4}{5}$ and $\cos y = \; \frac{12}{13}$

x is obtuse i.e sin x = + ve while cos x = + ve

$\cos x = \; \frac{3}{5} == \; \; gt; \cos x = -\; \frac{3}{5}\text{(obtuse)}$

$\sin \; y = \; \frac{5}{13}$

$\sin \; (x-y) = \sin \; x$ $\cos y - \cos x$ $\sin \; y$

$\sin(x-y) = \; \frac{4}{5} \times \; \frac{12}{13} - \left(-\; \frac{3}{5}\right) \times \; \frac{5}{13}$

$\sin(x-y) = \; \frac{48}{65} - \left(-\; \frac{3}{13}\right)$

$\therefore \sin \; (x-y) = \; \frac{48}{65} + \; \frac{3}{13} = \; \frac{63}{65}$