Evaluate : `cos 38^@ cos 52^@ - sin 38^@ sin 52^@`.

Answer

To evaluate the expression \( \cos 38^\circ \cos 52^\circ - \sin 38^\circ \sin 52^\circ \), we can use the cosine addition formula.

### Step-by-Step Solution:

1. **Identify the terms**: We have \( \cos 38^\circ \cos 52^\circ \) and \( -\sin 38^\circ \sin 52^\circ \).

2. **Use the cosine addition formula**: The cosine of the sum of two angles is given by:
\[ \cos(a + b) = \cos a \cos b - \sin a \sin b \]
Here, we can let \( a = 38^\circ \) and \( b = 52^\circ \).

3. **Apply the formula**: According to the formula,
\[ \cos 38^\circ \cos 52^\circ - \sin 38^\circ \sin 52^\circ = \cos(38^\circ + 52^\circ) \]

4. **Calculate the angle**: Now, we add the angles:
\[ 38^\circ + 52^\circ = 90^\circ \]

5. **Evaluate \( \cos 90^\circ \)**: We know that:
\[ \cos 90^\circ = 0 \]

6. **Final Result**: Therefore,
\[ \cos 38^\circ \cos 52^\circ - \sin 38^\circ \sin 52^\circ = 0 \]

### Conclusion:
The value of \( \cos 38^\circ \cos 52^\circ - \sin 38^\circ \sin 52^\circ \) is \( 0 \).