Question 27

Explanation

To solve the limit $\lim_{x \to 0} \left(\frac{1 - \cos 2x}{x \tan 2x}\right)$, use trigonometric identities

Using Trigonometric Identities

Use the identity $1 - \cos 2x = 2\sin^2 x$

Separating the Limit

Separate into several parts using limit properties

Use the fact that $\lim_{x \to 0} \frac{\sin x}{x} = 1$

Therefore, the value of $\lim_{x \to 0} \left(\frac{1 - \cos 2x}{x \tan 2x}\right) = 1$