solve the following expression `cos32^@ cdot cos28^@-sin32^@ cdot sin28^@`:

Options

A. 1
B. `1/2`
C. 0
D. can't be determined

Answer

To solve the expression \( \cos 32^\circ \cdot \cos 28^\circ - \sin 32^\circ \cdot \sin 28^\circ \), we can use a trigonometric identity.

### Step-by-step solution:

1. **Identify the Trigonometric Identity**:
We know from trigonometric identities that:
\[ \cos A \cdot \cos B - \sin A \cdot \sin B = \cos(A + B) \]
Here, \( A = 32^\circ \) and \( B = 28^\circ \).

2. **Apply the Identity**:
Substitute \( A \) and \( B \) into the identity:
\[ \cos 32^\circ \cdot \cos 28^\circ - \sin 32^\circ \cdot \sin 28^\circ = \cos(32^\circ + 28^\circ) \]

3. **Calculate the Angle**:
Now, calculate \( 32^\circ + 28^\circ \):
\[ 32^\circ + 28^\circ = 60^\circ \]

4. **Find the Cosine Value**:
Now, we need to find \( \cos 60^\circ \):
\[ \cos 60^\circ = \frac{1}{2} \]

5. **Conclusion**:
Therefore, the value of the expression \( \cos 32^\circ \cdot \cos 28^\circ - \sin 32^\circ \cdot \sin 28^\circ \) is:
\[ \frac{1}{2} \]

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