Find the domain of the function
`f(x) = (1)/(sqrt(1 - cos x))`

Answer

To find the domain of the function \( f(x) = \frac{1}{\sqrt{1 - \cos x}} \), we need to ensure that the expression inside the square root is positive, as the square root function is only defined for non-negative numbers, and we cannot have the denominator equal to zero.

### Step-by-step Solution:

1. **Identify the condition for the square root**:
We need \( 1 - \cos x > 0 \).

2. **Rearranging the inequality**:
This can be rewritten as:
\[ \cos x < 1 \]

3. **Understanding the cosine function**:
The cosine function, \( \cos x \), takes values in the range \([-1, 1]\). The only time \( \cos x \) equals 1 is when \( x = 2n\pi \) for any integer \( n \).

4. **Finding the points to exclude**:
Since we need \( 1 - \cos x \) to be greater than 0, we must exclude the points where \( \cos x = 1 \). Therefore, we exclude:
\[ x = 2n\pi \quad \text{where } n \in \mathbb{Z} \]

5. **Writing the domain**:
The domain of the function \( f(x) \) is all real numbers except the points where \( \cos x = 1 \):
\[ x \in \mathbb{R} \setminus \{ 2n\pi \,|\, n \in \mathbb{Z} \} \]

### Final Answer:
The domain of the function \( f(x) = \frac{1}{\sqrt{1 - \cos x}} \) is:
\[ x \in \mathbb{R} \setminus \{ 2n\pi \,|\, n \in \mathbb{Z} \} \]