The value of `cos1^o.cos2 ^o.cos3^o.....cos179^o` is equal to

Answer

To find the value of \( \cos 1^\circ \cdot \cos 2^\circ \cdot \cos 3^\circ \cdots \cos 179^\circ \), we can follow these steps:

### Step 1: Identify the range of angles
The product involves the cosine of angles from \( 1^\circ \) to \( 179^\circ \).

### Step 2: Recognize the symmetry in cosine
The cosine function has a property where \( \cos(180^\circ - x) = -\cos(x) \). This means:
- \( \cos 179^\circ = -\cos 1^\circ \)
- \( \cos 178^\circ = -\cos 2^\circ \)
- ...
- \( \cos 91^\circ = -\cos 89^\circ \)

### Step 3: Include \( \cos 90^\circ \)
Notice that \( \cos 90^\circ = 0 \). Since \( \cos 90^\circ \) is included in the product, it will result in the entire product being zero.

### Step 4: Conclude the result
Since multiplying any number by zero results in zero, we conclude that:
\[ \cos 1^\circ \cdot \cos 2^\circ \cdot \cos 3^\circ \cdots \cos 179^\circ = 0 \]

Thus, the value of \( \cos 1^\circ \cdot \cos 2^\circ \cdot \cos 3^\circ \cdots \cos 179^\circ \) is \( 0 \).

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