Limit as x->0, csc, cos HELP

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
:)

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Char. Limit
Gold Member
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:

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