Write the following function in the simplest form: `tan^-1 sqrt((1-cosx)/(1+cosx))`

Explanation

To simplify the function \( \tan^{-1} \sqrt{\frac{1 - \cos x}{1 + \cos x}} \), we can follow these steps:

### Step 1: Use Half-Angle Formulas
We start by applying the half-angle formulas for cosine:
- \( 1 - \cos x = 2 \sin^2 \frac{x}{2} \)
- \( 1 + \cos x = 2 \cos^2 \frac{x}{2} \)

### Step 2: Substitute in the Expression
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