What is the limit of (xcsc2x)/(cos5x) as x approaches 0?

[motorhead87]

Homework Statement

lim as x-> 0

(xcsc2x)/(cos5x)

Homework Equations

lim as x-> 0 (sinx)/x = 1

The Attempt at a Solution

(x(1/sin2x)) / (cos5x)

Not sure what I am supposed to do here! Thanks
:)

 

[Char. Limit]

Firstly, if this is true:

\lim_{x\rightarrow0} \frac{sin(x)}{x} = 1

Then can you figure out what this limit is?

\lim_{x\rightarrow0} \frac{x}{sin(x)}

And then if you use 2x instead of x, this limit should be just as easy:

\lim_{x\rightarrow0} \frac{2x}{sin(2x)}