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 a step-by-step approach.

### Step 1: Define the angle
Let \( \theta = \cos^{-1}(x) \). This implies that \( \cos(\theta) = x \).

### Step 2: Construct a right triangle
From the definition of cosine, we can construct a right triangle where:
- The adjacent side (base) is \( x \)
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