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. 

Note that $\csc (2x) = \frac{1}{\sin(2x)} = \frac{1}{2 \sin x \cos x}$, and $\tan x = \frac{\sin x}{\cos x}$.
So $$\lim_{x \to 0} \tan x \csc (2x) = \lim_{x \to 0} \frac{1}{2 \sin x \cos x} \frac{\sin x}{\cos x} = \lim_{x \to 0} \frac{1}{2 \cos^2 x} = \frac{1}{2}$$
