I have following function limit to find:
$$
\lim_{x\to 0} \frac{\sqrt{2+\sin(6x)}-\sqrt{2-\sin(6x)}}{\tan(2x)}
$$
and the result with all steps is as following(excuse the image):
I don't understand the step where $2\sin(6x)\cos(2x)$ and $\sin(2x)$ becomes $2\frac{\sin(6x)}{x}$ and $\frac{\sin(2x)}{x}$. What I am missing?