Convert the products into sum or difference.
`2 sin 48^(@) cos 12 ^(@)`

Answer

To convert the product \( 2 \sin 48^\circ \cos 12^\circ \) into a sum or difference, we can use the trigonometric identity:

\[ 2 \sin x \cos y = \sin(x + y) + \sin(x - y) \]

### Step-by-step Solution:

1. **Identify the values of \( x \) and \( y \)**:
- Here, \( x = 48^\circ \) and \( y = 12^\circ \).

2. **Apply the identity**:
- Substitute \( x \) and \( y \) into the identity:
\[ 2 \sin 48^\circ \cos 12^\circ = \sin(48^\circ + 12^\circ) + \sin(48^\circ - 12^\circ) \]

3. **Calculate the angles**:
- Calculate \( 48^\circ + 12^\circ \):
\[ 48^\circ + 12^\circ = 60^\circ \]
- Calculate \( 48^\circ - 12^\circ \):
\[ 48^\circ - 12^\circ = 36^\circ \]

4. **Write the final expression**:
- Substitute the calculated angles back into the equation:
\[ 2 \sin 48^\circ \cos 12^\circ = \sin 60^\circ + \sin 36^\circ \]

### Final Answer:
\[ 2 \sin 48^\circ \cos 12^\circ = \sin 60^\circ + \sin 36^\circ \]