To find which of the given expressions has the same value as \(\cos 30^\circ\), we can first calculate \(\cos 30^\circ\):
\[ \cos 30^\circ = \frac{\sqrt{3}}{2} \]
Now let's evaluate the other expressions:
-
\(\cos \frac{\pi}{6}\): \[ \cos \frac{\pi}{6} = \cos 30^\circ = \frac{\sqrt{3}}{2} \]
-
\(\sin 30^\circ\): \[ \sin 30^\circ = \frac{1}{2} \]
-
\(\sin \frac{\pi}{6}\): \[ \sin \frac{\pi}{6} = \sin 30^\circ = \frac{1}{2} \]
-
\(\cos 60^\circ\): \[ \cos 60^\circ = \frac{1}{2} \]
Thus, the only expression that is equal to \(\cos 30^\circ\) (or \(\frac{\sqrt{3}}{2}\)) is:
\(\cos \frac{\pi}{6}\)
So, the correct answer is \(\cos \frac{\pi}{6}\).