Prove that `cos (tan^(-1) (sin (cot^(-1) x))) = sqrt((x^(2) + 1)/(x^(2) + 2))`

Explanation

To prove that \( \cos(\tan^{-1}(\sin(\cot^{-1} x))) = \sqrt{\frac{x^2 + 1}{x^2 + 2}} \), we will follow these steps:

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

### Step 2: Create a right triangle
From the definition of cotangent, we can represent this in a right triangle where:
- The adjacent side (base) is \( x \)
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