$\displaystyle \lim_{x\to0} \frac{cot (2x)}{csc (x)}$

$\displaystyle \lim_{x\to0} \frac{sinx cos(2x)}{sin (2x)}$

$\displaystyle \lim_{x\to0} \frac{sinx cos(2x)}{2sinxcosx}$

$\displaystyle \lim_{x\to0} \frac{cos(2(0))}{2cos(0)}$

= $\displaystyle \frac{1}{2}$

correct?