If `0< x< 1`,then `tan^(-1)(sqrt(1-x^2)/(1+x))` is equal to

Options

A. `1/2 cos^(-1)x`
B. `cos^(-1)sqrt(1+x)/(2)`
C. `sin^(-1)sqrt(1-x)/(2)`
D. all the above

Explanation

To solve the problem, we need to find the value of \( \tan^{-1} \left( \frac{\sqrt{1 - x^2}}{1 + x} \right) \) for \( 0 < x < 1 \).

### Step-by-Step Solution:

1. **Substitution**: Let \( x = \cos \theta \).
- Since \( 0 < x < 1 \), it follows that \( 0 < \theta < \frac{\pi}{2} \).

2. **Rewrite the expression**:
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