The given expression is:

\[
\sin 30^\circ \cdot \cos 60^\circ + \sin 60^\circ \cdot \cos 30^\circ
\]

Using the known trigonometric values:
- \(\sin 30^\circ = \frac{1}{2}\)
- \(\cos 60^\circ = \frac{1}{2}\)
- \(\sin 60^\circ = \frac{\sqrt{3}}{2}\)
- \(\cos 30^\circ = \frac{\sqrt{3}}{2}\)

Now, substitute these values into the expression:

\[
\frac{1}{2} \cdot \frac{1}{2} + \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}
\]

Simplifying:

\[
\frac{1}{4} + \frac{3}{4} = 1
\]

Thus, the value of the expression is:

\[
1
\]

Would you like further details or have any questions? Here are some related questions to deepen your understanding:

1. What is the general formula for the sum of angles in sine?
2. How do you derive the values of common angles in trigonometry?
3. Can you express \(\sin(A + B)\) using \(\sin A\) and \(\sin B\)?
4. What is the significance of complementary angles in trigonometry?
5. How can trigonometric identities simplify complex expressions?

**Tip:** Memorizing the values of sine and cosine for standard angles (like 30°, 45°, and 60°) can save time during calculations.

Learn how to simplify the trigonometric expression sin 30° cos 60° + sin 60° cos 30° using fundamental trigonometric values and identities. This solution explains key concepts in trigonometry, such as complementary angles and common angle identities. Suitable for students in Grades 9-10.

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