Prove that `sin (cot^(-1) (tan (cos^(-1) x))) = x, x gt 0`

Explanation

To prove that \( \sin(\cot^{-1}(\tan(\cos^{-1} x))) = x \) for \( x > 0 \), we will follow these steps:

### Step 1: Start with the left-hand side
We need to prove that:
\[ \sin(\cot^{-1}(\tan(\cos^{-1} x))) = x \]

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