b) If $\sin (x)=\frac{1}{3}$ and $\sec (y)=\frac{5}{4}$, where $0 \leq x \leq \frac{\pi}{2}$ and $0 \leq y \leq \frac{\pi}{2}$ , evaluate the expression $\cos (x+y)$.

Step 1 ：Given that \(\sin(x) = \frac{1}{3}\) and \(\sec(y) = \frac{5}{4}\), we can find \(\cos(x)\), \(\cos(y)\), and \(\sin(y)\) using the trigonometric identities.

Step 2 ：Using the identity \(\cos(x+y) = \cos(x)\cos(y) - \sin(x)\sin(y)\), we can plug in the values we found to get \(\cos(x+y)\approx 0.5542\).

Step 3 ：\boxed{0.5542}