Find Limits using Trig Functions

[Roxanne]

I am having a problem with this:

find limit if limit exists

lim x-tanx
x->0 sinx

I know this much
x-sinx/cosx
sin x

but I am stuck from here

 

[Deleted member 4993]

I am having a problem with this:

find limit if limit exists

lim x-tanx
x->0 sinx

I know this much
x-sinx/cosx
sin x

but I am stuck from here

What is:

\(\displaystyle \frac{\tan(x)}{\sin(x)} \, = \, ???\)

What is the limit of that trigonometric function as x -> 0?

As x-> 0 , what is the limit of

\(\displaystyle \frac{x}{sin(x)}\)