finding limit, as x goes to 0, of x cos(x) csc(x)

[f1tz22]

I've been stuck on this for a while.
Lim x cosx cscx
x->0
and what I've done is re-wrote that as
lim xcosx/sinx
x->0
I'm stuck here and any help would be appreciated.

 

[royhaas]

Re: lim of xcosxcscx

Suppose you write this as \(\displaystyle \frac{x}{\sin(x)}\cos(x)\). Does it look more familiar now?

 

[f1tz22]

Re: lim of xcosxcscx

Haha wow thanks. I knew it was something easy. Just to make sure, the limit ends up being 1 correct?
Thanks again.

 

[royhaas]

Re: lim of xcosxcscx

Yes, the limit is 1.