1. **Problem Statement:** Evaluate the expression $2 \sin(34^\circ) \cos(34^\circ)$.\n\n2. **Formula Used:** The double-angle identity for sine states that: $$2 \sin(\theta) \cos(\theta) = \sin(2\theta)$$ This identity allows us to simplify the product of sine and cosine into a single sine function with double the angle. \n3. **Apply the formula:** Substitute $\theta = 34^\circ$: $$2 \sin(34^\circ) \cos(34^\circ) = \sin(2 \times 34^\circ) = \sin(68^\circ)$$ \n4. **Evaluate the sine:** Using a calculator or sine table: $$\sin(68^\circ) \approx 0.9272$$ \n5. **Conclusion:** The value of $2 \sin(34^\circ) \cos(34^\circ)$ is approximately $0.9272$. \nThis shows how double-angle identities simplify trigonometric expressions by converting products into single trigonometric functions, making evaluation easier.