Find the value of `cos1^(@).cos2^(@).cos3^(@).cos90^(@)`

Options

A. `-1`
B. 0
C. 1
D. `alpha`

Answer

To solve the question, we need to find the value of the expression:

\[ \cos(1^\circ) \cdot \cos(2^\circ) \cdot \cos(3^\circ) \cdot \cos(90^\circ) \]

### Step-by-Step Solution:

1. **Identify the values of the cosine functions:**
- We know that:
\[ \cos(90^\circ) = 0 \]
- The values of \(\cos(1^\circ)\), \(\cos(2^\circ)\), and \(\cos(3^\circ)\) are not needed for the final answer since we will multiply by \(\cos(90^\circ)\).

2. **Multiply the cosine values:**
- The expression can be rewritten as:
\[ \cos(1^\circ) \cdot \cos(2^\circ) \cdot \cos(3^\circ) \cdot 0 \]

3. **Apply the multiplication property:**
- According to the multiplication property of numbers, any number multiplied by zero is zero:
\[ \cos(1^\circ) \cdot \cos(2^\circ) \cdot \cos(3^\circ) \cdot 0 = 0 \]

4. **Conclusion:**
- Therefore, the value of the expression is:
\[ 0 \]

### Final Answer:
\[ \cos(1^\circ) \cdot \cos(2^\circ) \cdot \cos(3^\circ) \cdot \cos(90^\circ) = 0 \]