How to get $\lim_{x\to 0}\frac{x}{\sin x} =1$ from $\lim_{x\to 0}\frac{\sin x}{x} =1$? We know the identity that 
$$\lim_{x\to 0}\frac{\sin x}{x} =1$$
However in many solved examples that I was going through , I came across the identity 
$$\lim_{x\to 0}\frac{x}{\sin x} =1$$
Although  it was never formally mentioned anywhere in the text . How does the previous identity imply this? 
Does it mean that as $x$ becomes very small the value of $\sin x$ is approximately equal to the value of $x$ so the value of both of $\frac{x}{\sin x}$ and $\frac{\sin x}{x}$ tends to $1$?

Simply note that
$$\frac{x}{\sin x}=\frac1{\frac{\sin x}{x}}\to \frac11=1$$
