`cos 1^(@)cos2^(@) cos3^(@)`..... `cos 180^(@)`.......

Answer

To solve the problem of finding the value of the product \( \cos(1^\circ) \cdot \cos(2^\circ) \cdot \cos(3^\circ) \cdots \cos(180^\circ) \), we can follow these steps:

### Step 1: Identify the range of angles
We are considering the product of cosines from \( \cos(1^\circ) \) to \( \cos(180^\circ) \).

### Step 2: Recognize the value of \( \cos(90^\circ) \)
We know that \( \cos(90^\circ) = 0 \).

### Step 3: Analyze the impact of \( \cos(90^\circ) \)
Since the product includes \( \cos(90^\circ) \), which is equal to 0, it will affect the entire product.

### Step 4: Conclude the result
When multiplying any number by 0, the result is always 0. Therefore, the entire product \( \cos(1^\circ) \cdot \cos(2^\circ) \cdot \cos(3^\circ) \cdots \cos(180^\circ) \) will equal 0.

### Final Answer
Thus, the value of \( \cos(1^\circ) \cdot \cos(2^\circ) \cdot \cos(3^\circ) \cdots \cos(180^\circ) = 0 \).

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