Show $$\dfrac{\sin(x)\cos^{n}(x)}{1-\cos(x)}\sim_{x\to 0^+}\dfrac{x}{\frac{x^2}{2}}$$ by strating from the left side and get the right side i don't want to use
$$f\sim g \iff \dfrac{f}{g}\underset{}{\overset{}{\longrightarrow}} 0$$
My thoughts:
$$\sin(x)\sim_{x\to 0}x$$ $$1-\cos(x)\sim_{x\to 0}\dfrac{x^2}{2} $$
how can i apply this since there is $\cos^{n}(x)$ i know it's $\cos^{n}(x)\leq 1$