Limits of Trigonometric Functions

If ${\lim }_{x\to c}g(x)=0$

${\lim }_{x\to c}\frac{\sin (g(x))}{g(x)}={\lim }_{x\to c}\frac{g(x)}{\sin (g(x))}=1$ ${\lim }_{x\to c}\frac{\tan (g(x))}{g(x)}={\lim }_{x\to c}\frac{g(x)}{\tan (g(x))}=1$

In Particular,

When $c=0$ and $g(x)=x$, ${\lim }_{x\to 0}\frac{\sin (x)}{x}={\lim }_{x\to 0}\frac{x}{\sin (x)}=1$ ${\lim }_{x\to 0}\frac{\tan (x)}{x}={\lim }_{x\to 0}\frac{x}{\tan (x)}=1$