The given trigonometric expression is:

$\sin(30^\circ - x) \cdot \cos(x) + \cos(30^\circ - x) \cdot \sin(x)$

This expression can be simplified using the sum of angles identity for sine. The identity is:

$\sin(A + B) = \sin(A) \cdot \cos(B) + \cos(A) \cdot \sin(B)$

In this case, compare the given expression to the sine identity:

$\sin((30^\circ - x) + x) = \sin(30^\circ)$

Thus, the expression simplifies to:

$\sin(30^\circ) = \frac{1}{2}$

Therefore, the simplified value of the expression is $\frac{1}{2}$.

---

Do you want further details or have any questions? Here are some related questions to extend your understanding:

1. What is the general formula for sine and cosine of sums and differences of angles?
2. How can you apply other angle sum identities (like cosine) to different expressions?
3. What is the importance of the unit circle in solving trigonometric problems?
4. How do we find exact values for trigonometric functions of special angles (e.g., 30°, 45°, 60°)?
5. Can you prove the angle sum identity for sine using geometric or algebraic methods?

Tip: Memorizing key trigonometric identities like sum and difference formulas can simplify complex expressions quickly!