Limit of a trigonometric function without l'hopitals rule?

[stony]

Homework Statement

lim of (sin(x)/(x+sin(x)) as x approaches 0

Homework Equations

none

The Attempt at a Solution

I tried using trigonometric identites to figure it out but I can't do it, and when I looked up help for it I only found solutions that utilize the l'hopitals rule. I have to know how to do these questions without this rule, can someone at least get me started in the right direction please? Thanks.

 

[pymn_nzr]

you can use Taylor series...
http://en.wikipedia.org/wiki/Taylor_series

 

[vela]

Try dividing the top and bottom by x.