Question Detail
Question
Evaluate the limit of \( \frac{\tan x}{\sin 2x} \) as \( x \) approaches \( \pi \).
Correct Answer
Option B is the correct answer.
Detailed Explanation
Using ( \tan x = \frac{\sin x}{\cos x} ) and ( \sin 2x = 2\sin x \cos x ), the expression simplifies to ( \frac{1}{2 \cos^2 x} ). At ( x = \pi ), ( \cos(\pi) = -1 ), so ( \frac{1}{2(-1)^2} = \frac{1}{2} ).
Hint
Example 15.