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 is C

Cos (x + y) 

= cos x cos y - sin x sin y

cos (x + y) = \(\frac{4}{5} \times \frac{24}{25} - \frac{3}{5} \times \frac{7}{25}\)

= \(\frac{96}{125} - \frac{21}{125} = \frac{96 - 21}{125}\)

= \(\frac{75}{125}\)

= \(\frac{3}{5}\)