To determine which of the expressions is equal to \(\cos 30^\circ\), we first need to calculate the value of \(\cos 30^\circ\).
The cosine of \(30^\circ\) is given by:
\[ \cos 30^\circ = \frac{\sqrt{3}}{2} \]
Now, we will evaluate the other expressions one by one.
A. \(\sin 30^\circ\)
\[
\sin 30^\circ = \frac{1}{2}
\]
This is not equal to \(\frac{\sqrt{3}}{2}\).
B. \(\cos \frac{\pi}{6}\)
Since \(\frac{\pi}{6}\) is equivalent to \(30^\circ\),
\[
\cos \frac{\pi}{6} = \cos 30^\circ = \frac{\sqrt{3}}{2}
\]
This is equal to \(\frac{\sqrt{3}}{2}\).
C. \(\sin \frac{\pi}{6}\)
Since \(\frac{\pi}{6}\) is equivalent to \(30^\circ\),
\[
\sin \frac{\pi}{6} = \frac{1}{2}
\]
This is not equal to \(\frac{\sqrt{3}}{2}\).
D. \(\cos 60^\circ\)
The cosine of \(60^\circ\) is given by:
\[
\cos 60^\circ = \frac{1}{2}
\]
This is not equal to \(\frac{\sqrt{3}}{2}\).
Now, we can see that among the choices given, only B. \(\cos \frac{\pi}{6}\) is equal to \(\cos 30^\circ\).
Thus, the answer is: \[ \text{B. } \cos \frac{\pi}{6} \]