Question

\[ \lim_{x \to \infty} \frac{1 - \tan\left(\frac{x}{2}\right)}{1 + \tan\left(\frac{x}{2}\right)} = ? \]

• A. \( \frac{1}{8} \)
• B. 0
• C. \( \frac{1}{32} \)
• D. \( \infty \)

Hint:

Use trigonometric identities and limits to simplify expressions and calculate their values as \( x \to \infty \).

Answer 1

The Correct Option is C

Step 1: Simplify the expression.
Using trigonometric identities, we simplify the expression and calculate the limit, which results in \( \frac{1}{32} \).
Thus, the correct answer is (3).