I would like to evaluate the limit $$lim_{xto0}frac{2xsin(x)}{1-cos(x)}$$ It can be done with L’Hospital, but I would like to know if it is possible to do so without L’Hospital. I tried multiplying through by the conjugate of the denominator, which leads me to $$lim_{xto0}frac{2x(1+cos(x))}{sin(x)}$$ which is not very helpful, because it is still $0/0$. Any help would be much appreciated, thanks!