If X = \(\frac{3}{5}\) and cos y = \(\frac{24}{25}\), where X and Y are acute, find the value of cos (X + Y).
- \(\frac{117}{125}\)
- \(\frac{24}{25}\)
-
\(\frac{3}{5}\)
- \(\frac{7}{25}\)
The correct answer is: C
Explanation
Cos (x + y)
= cos x cos y - sin x sin y
cos (x + y) = \(\frac{4}{5} \times \frac{24}{25} - \frac{3}{5} \times \frac{7}{25}\)
= \(\frac{96}{125} - \frac{21}{125} = \frac{96 - 21}{125}\)
= \(\frac{75}{125}\)
= \(\frac{3}{5}\)