Evaluate :
`2 sin 15 ^(@) cos 15 ^(@)`

Answer

To evaluate \( 2 \sin 15^\circ \cos 15^\circ \), we can use the double angle identity for sine. The identity states that:

\[ \sin 2\theta = 2 \sin \theta \cos \theta \]

### Step-by-step Solution:

1. **Identify the angle**: Here, we have \( \theta = 15^\circ \).

2. **Apply the double angle identity**: According to the identity, we can rewrite \( 2 \sin 15^\circ \cos 15^\circ \) as:
\[ 2 \sin 15^\circ \cos 15^\circ = \sin(2 \times 15^\circ) \]

3. **Calculate \( 2 \times 15^\circ \)**: This gives us:
\[ 2 \times 15^\circ = 30^\circ \]

4. **Substitute back into the equation**: Now we have:
\[ 2 \sin 15^\circ \cos 15^\circ = \sin 30^\circ \]

5. **Find the value of \( \sin 30^\circ \)**: We know from trigonometric values that:
\[ \sin 30^\circ = \frac{1}{2} \]

6. **Conclusion**: Therefore, we can conclude that:
\[ 2 \sin 15^\circ \cos 15^\circ = \frac{1}{2} \]

### Final Answer:
\[ \frac{1}{2} \]