$\lim \limits_{x \to 2} \large\frac{e^x-e^{\sin x}}{2(x- \sin x)}$

Question

\[\begin {array} {1 1} (a)\;-\frac{1}{2} & \quad (b)\;\frac{1}{2} \\ (c)\;1 & \quad (d)\;\frac{3}{2} \end {array}\]