algebra precalculus - How can I find this limit? $lim_{xto0}left(frac{xcsc(2x)}{3cos(5x)}right)$

$$\lim_{x\to0}\left(\frac{x\csc(2x)}{3\cos(5x)}\right)$$

My attempt was just turning csc to 1/sin, how can I solve this

Answer

for $x$ reaching $0$ $\sin {x} = x$

then

$$\lim_{x\to0}\frac {x}{\sin{x}} = 1$$

$$\lim_{x\to0} \cos {x} = 1$$

So your limit is equal to $\frac{1}{6}$ if I'm not mistakening