Find $\displaystyle \lim_{x \to 0} \frac{x \cdot \operatorname{cosec}(2x)}{\cos(5x)}$ I am having difficulties to find the limit for
$$\lim_{x \to 0} \frac{x \cdot \operatorname{cosec}(2x)}{\cos(5x)}$$
I tried to get rid of $ \operatorname{cosec} $ fist
$$\lim_{x \to 0} \frac{\dfrac{x}{\sin(2x)}}{\cos(5x)}$$
Probably I should get it to a point where I could make use of $\displaystyle \lim_{x \to 0} \frac{\sin(x)}{x} = 1$ but I don't know how to continue.
Maybe if one could give me a hint for the next step?

HINT : You can use $\lim_{x\to 0}\frac{\sin(2x)}{2x}=1.$
