limit, as x tends to 0, of cosx - 1 / sinx

[maeveoneill]

just wondering if someone could help me some this limit

lim = cosx -1/ sinx
x -> 0

i am guessing i need trig identities.. but i just dont know which one to use.. even that would be enough for me to figure out the rest..

Thank youuu

 

[pka]

\(\displaystyle \L \begin{array}{rcl}
\frac{{\cos (x) - 1}}{{\sin (x)}}\frac{{\cos (x) + 1}}{{\cos (x) + 1}} & = & \frac{{\cos ^2 (x) - 1}}{{\left( {\cos (x) + 1} \right)\sin (x)}} \\
& = & \frac{{ - \sin ^2 (x)}}{{\left( {\cos (x) + 1} \right)\sin (x)}} \\
& = & \frac{{ - \sin (x)}}{{\left( {\cos (x) + 1} \right)}} \\
\end{array}\)