WAEC - Further Mathematics (2021 - No. 24)

If sin x = \(\frac{12}{13}\) and sin y = \(\frac{4}{5}\), where x and y are acute angles, find cos (x + y)

\(\frac{48}{65}\)

\(\frac{13}{15}\)

\(\frac{-33}{65}\)

\(\frac{-48}{65}\)

From Pythagoras' theorem

when sin x = \(\frac{12}{13}\), cos x = \(\frac{5}{13}\)

Using cos (x + y) = cosx cosy - sinxsiny

\(\frac{5}{13}\) * \(\frac{3}{5}\) - \(\frac{12}{13}\) * \(\frac{4}{5}\)

= \(\frac{-33}{65}\)