The value of `cos38^(@)cos52^(@)-sin38^(@)sin52^(@)` is :

Options

A. `-1`
B. 1
C. 0
D. None of these

Answer

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

### Step-by-Step Solution:

1. **Identify the expression**: The expression we have is \( \cos 38^\circ \cos 52^\circ - \sin 38^\circ \sin 52^\circ \).

2. **Use the cosine angle addition formula**: Recall that the cosine of the sum of two angles can be expressed as:
\[ \cos(a + b) = \cos a \cos b - \sin a \sin b \]
In our case, we can let \( a = 38^\circ \) and \( b = 52^\circ \).

3. **Apply the formula**: According to the formula:
\[ \cos(38^\circ + 52^\circ) = \cos 38^\circ \cos 52^\circ - \sin 38^\circ \sin 52^\circ \]
Thus, we can rewrite our expression as:
\[ \cos(38^\circ + 52^\circ) = \cos(90^\circ) \]

4. **Calculate \( \cos(90^\circ) \)**: The value of \( \cos(90^\circ) \) is:
\[ \cos(90^\circ) = 0 \]

5. **Final answer**: Therefore, the value of the original expression \( \cos 38^\circ \cos 52^\circ - \sin 38^\circ \sin 52^\circ \) is:
\[ 0 \]