Prove that `tan^(-1)(sqrt((1-cosx)/(1+cosx))=x/2, x lt pi`.

Explanation

To prove that

\[ \tan^{-1}\left(\sqrt{\frac{1 - \cos x}{1 + \cos x}}\right) = \frac{x}{2}, \quad x < \pi, \]

we will follow these steps:

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