$\large \lim_{x->0}\frac{\left ( 1-cosx \right )}{2}$
=>$\large \lim_{x->0}\frac{\left ( 1-cosx \right )}{x}*\frac{x}{2}$
=$\large \lim_{x->0}\frac{\left ( 1-cosx \right )}{x}\lim_{x->0}*\frac{x}{2}$ [$\large \lim_{x->0}\frac{\left ( 1-cosx \right )}{x}=0$]
=$0*0$
=$0$