The value of `cos0 cos1^(@)cos2^(@)` ……………. `cos179^(@) cos180^(@)` is :

Options

A. `-1`
B. `0`
C. `1`
D. `(1+sqrt(2))/(2)`

Explanation

To find the value of the product \( \cos 0^\circ \cos 1^\circ \cos 2^\circ \ldots \cos 179^\circ \cos 180^\circ \), we can follow these steps:

### Step 1: Understand the cosine function
The cosine function, \( \cos \theta \), is defined for angles from \( 0^\circ \) to \( 180^\circ \). Notably, \( \cos 90^\circ = 0 \).

### Step 2: Identify the product
We are looking at the product:
\[ P = \cos 0^\circ \cos 1^\circ \cos 2^\circ \ldots \cos 179^\circ \cos 180^\circ \]

### Step 3: Notice the presence of \( \cos 90^\circ \)
In the product, we can see that \( \cos 90^\circ \) is included. Since \( \cos 90^\circ = 0 \), this means that the entire product will be zero because multiplying any number by zero results in zero.

### Step 4: Conclude the result
Therefore, we can conclude that:
\[ P = 0 \]

### Final Answer
The value of \( \cos 0^\circ \cos 1^\circ \cos 2^\circ \ldots \cos 179^\circ \cos 180^\circ \) is \( 0 \).