To find which expression has the same value as \(\cos 30^\circ\), we first calculate \(\cos 30^\circ\):
\[ \cos 30^\circ = \frac{\sqrt{3}}{2} \]
Now, we check each of the given expressions.
-
sin 30° cos 60°:
- \(\sin 30^\circ = \frac{1}{2}\)
- \(\cos 60^\circ = \frac{1}{2}\)
- Therefore, \(\sin 30^\circ \cos 60^\circ = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\)
-
cos \(\frac{\pi}{6}\):
- \(\cos \frac{\pi}{6} = \cos 30^\circ = \frac{\sqrt{3}}{2}\)
-
sin \(\frac{\pi}{6}\):
- \(\sin \frac{\pi}{6} = \frac{1}{2}\)
Now check sin \(\frac{\pi}{6}\) cos \(\frac{\pi}{6}\): \[ \sin \frac{\pi}{6} \cos \frac{\pi}{6} = \frac{1}{2} \times \frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{4} \]
After evaluating the expressions, we see that:
- \(\sin 30^\circ \cos 60^\circ = \frac{1}{4}\)
- \(\cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}\)
- \(\sin \frac{\pi}{6} \cos \frac{\pi}{6} = \frac{\sqrt{3}}{4}\)
The only expression that has the same value as \(\cos 30^\circ\) is
cos \(\frac{\pi}{6}\), which is equal to \(\frac{\sqrt{3}}{2}\).