We know that:
\[
\sin 30^\circ = \frac{1}{2} \quad \text{and} \quad \cos 60^\circ = \frac{1}{2}
\]
Now, we calculate:
\[
\sin 30^\circ + \cos 60^\circ = \frac{1}{2} + \frac{1}{2} = 1
\]
Thus, the value of \( \sin 30^\circ + \cos 60^\circ \) is 1. Therefore, the correct answer is option (1).