If `0ltxlt1` then `sqrt(1+x^(2))[{x cos (cot^(-1)x)+sin(cot^(-1)x}^(2)-1]^(1/2)`

Options

A. `(x)/sqrt(1+x^(2))`
B. x
C. `xsqrt(1+x^(2))`
D. `sqrt(1+x^(2))`

Explanation

To solve the given expression \( \sqrt{1+x^2} \left[ x \cos(\cot^{-1} x) + \sin(\cot^{-1} x) \right]^2 - 1 \), we will follow these steps:

### Step-by-Step Solution:

1. **Let \( \theta = \cot^{-1}(x) \)**:
- By definition, \( \cot(\theta) = x \).
- This implies that in a right triangle, the adjacent side is \( x \) and the opposite side is \( 1 \).

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