If sin x = \(\frac{12}{13}\) and sin y = \(\frac{4}{5}\), where x and y are
FURTHER MATHEMATICS
WAEC 2021
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. \(\frac{-48}{65}\)
Correct Answer: C. \(\frac{-33}{65}\)
Explanation
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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