WAEC 2020 · Paper 1 · Q15

If $\sin X = \frac{3}{5}$ and $\cos Y = \frac{24}{25}$ , where $X$ and $Y$ are acute, find the value of $\cos(X + Y)$ .

Worked solution (try it first)

Both angles are acute, so from right-angled triangles (3, 4, 5 and 7, 24, 25): $\cos X = \frac{4}{5}$ and $\sin Y = \frac{7}{25}$ .
Use $\cos(X + Y) = \cos X \cos Y - \sin X \sin Y$ : this is $\frac{4}{5} \times \frac{24}{25} - \frac{3}{5} \times \frac{7}{25}$ .
That is $\frac{96}{125} - \frac{21}{125} = \frac{75}{125}$
$= \frac{3}{5}$ , option C.