If X = \(\frac{3}{5}\) and cos y = \(\frac{24}{25}\), where X and Y are acute,
FURTHER MATHEMATICS
WAEC 2020
If X = \(\frac{3}{5}\) and cos y = \(\frac{24}{25}\), where X and Y are acute, find the value of cos (X + Y).
- A. \(\frac{117}{125}\)
- B. \(\frac{24}{25}\)
- C. \(\frac{3}{5}\)
- D. \(\frac{7}{25}\)
Correct Answer: C. \(\frac{3}{5}\)
Explanation
Cos (x + y)
= cos x cos y - sin x sin y
cos (x + y) = \(\frac{4}{5} \times \frac{24}{25} - \frac{3}{5} \times \frac{7}{25}\)
= \(\frac{96}{125} - \frac{21}{125} = \frac{96 - 21}{125}\)
= \(\frac{75}{125}\)
= \(\frac{3}{5}\)
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