Chapter 2 - Limits - 2.6 Trigonometric Limits - Exercises - Page 77: 17

$$1$$

\begin{align*} \lim _{x \rightarrow 0} \frac{\tan x}{x}&=\lim _{x \rightarrow 0} \frac{\sin x}{x}\frac{1}{\cos x}\\ &=\lim _{x \rightarrow 0} \frac{\sin x}{x}\lim _{x \rightarrow 0}\frac{1}{\cos x}\\ &=1. \end{align*}