Help with finding the $\lim_{x\to 0} \tan x \csc (2x)$ So I am trying to figure out the limit
$$\lim_{x\to 0} \tan x  \csc (2x)$$
I am not sure what action needs to be done to solve this and would appreciate any help to solving this. 

$$
\csc{2x} = \frac{1}{\sin 2x} = \frac{1}{2 \sin x \cos x}
$$
Then 
$$
\lim_{x\rightarrow 0} \frac{\sin x}{\cos x} \frac{ 1}{2 \sin x \cos x}= 
\lim_{x\rightarrow 0} \frac{1}{2 \cos^2 x} = \frac{1}{2}
$$
