=\displaystyle \lim_{x \to 0} {\left(\frac{\frac{e^x-1}{x}}{\frac{\sin x-\textrm{sh} 2x}{x}}+\frac{\frac{1-e^{2x}}{2x}}{\frac{\sin x-\textrm{sh} 2x}{2x}}}\right)=\lim_{x \to 0} {\left(\frac{1}{\frac{\sin x}{x}-2\frac{\textrm{sh} 2x}{2x}}-\frac{1}{\frac{\sin x}{2x}-\frac{\textrm{sh} 2x}{2x}}}\right)=1