Sove `[cot^(-1) x] + [cos^(-1) x] =0`, where `[.]` denotes the greatest integer function

Explanation

To solve the equation \([ \cot^{-1} x ] + [ \cos^{-1} x ] = 0\), where \([.]\) denotes the greatest integer function, we will follow these steps:

### Step 1: Understand the ranges of the functions involved
The function \(\cot^{-1} x\) has a range of \((0, \pi)\) and the function \(\cos^{-1} x\) has a range of \([0, \pi]\).

### Step 2: Analyze the greatest integer function
The greatest integer function \([y]\) gives the largest integer less than or equal to \(y\). For both \(\cot^{-1} x\) and \(\cos^{-1} x\), since their ranges are between \(0\) and \(\pi\), we can conclude that:
- \([ \cot^{-1} x ]\) can be \(0\) or \(1\) (since \(\pi \approx 3.14\)).
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