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

  • A \(\frac{48}{65}\)
  • B \(\frac{13}{15}\)
  • C \(\frac{-33}{65}\)
  • D \(\frac{-48}{65}\)
waec 2021furthermathematics

The correct answer is C. \(\frac{-33}{65}\)

From Pythagoras' theorem

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

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

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

= \(\frac{-33}{65}\)

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