WAEC Further Mathematics 2017 Paper

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

Given $\sin$ of an angle implies we have the value of the opposite and hypotenuse of the right-angled triangle. We find the adjacent side using Pythagoras' theorem.

$Adj^2 = Hyp^2 - Opp^2$

For triangle with angle x, $adj = \sqrt{13^2 - 5^2} = \sqrt{144} = 12$

For triangle with angle y, $adj = \sqrt{17^2 - 8^2} = \sqrt{225} = 15$

$\therefore \cos x = \frac{12}{13}; \cos y = \frac{15}{17}$

$\cos(x+y) = \left(\frac{12}{13} \times \frac{15}{17}\right) - \left(\frac{5}{13} \times \frac{8}{17}\right) = \frac{180}{221} - \frac{40}{221}$

= $\frac{140}{221}$