limits - Calculate $lim_{xto 0} frac{x-sin x} {1-cos x}$

Calculate the limit without using de l'Hopital:

$$\lim_{x\to 0} \frac{x-\sin x} {1-\cos x}$$ I want to use the limit: $$\lim_{x\to 0} \frac{\sin x}{x}=1$$ but I don't know how to do it.

I manipulated the expression to get

$$\lim_{x\to 0} \frac{x}{x-\sin x}-\lim_{x\to 0} \frac{\sin x} {1-\cos x}$$ but I don't know where to go from here.