Find the sum of roots the equation `cos^(-1)(cos x)=[x],[*]` denotes the greatest integer funtions.

Explanation

To solve the equation \( \cos^{-1}(\cos x) = [x] \), where \([x]\) denotes the greatest integer function, we will follow these steps:

### Step 1: Understand the Function
The function \( \cos^{-1}(\cos x) \) gives us the principal value of the angle \( x \) in the range \([0, \pi]\). However, since the cosine function is periodic, we need to consider the periodic nature of cosine.

### Step 2: Determine the Range of \( \cos^{-1}(\cos x) \)
For any real number \( x \), the value of \( \cos^{-1}(\cos x) \) can be expressed as:
\[
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