Let's solve the limit:

\[
\lim_{x \to \frac{x}{2}} \frac{1 + \sin x}{1 - \cos x}
\]

To clarify, I assume you intended to write the limit as \( x \) approaches 0 (or another value), not \( x \to \frac{x}{2} \). If that's correct, the limit should look like:

\[
\lim_{x \to 0} \frac{1 + \sin x}{1 - \cos x}
\]

Is this the correct interpretation of your question? If so, I can continue with solving the limit.

Learn how to evaluate the limit as x approaches 0 of (1 + sin x) / (1 - cos x) with a detailed step-by-step solution. This problem involves trigonometric identities and limits. Suitable for advanced high school or college-level students.

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