I need your expertise once again now that I've encountered a problem that I can't really figure out and Google wasn't doing much to help.

I have to figure out what the limit of 1/x-cos(x)/sin(x) when x approaches pi-.

I know that the answer is infinity but when i try to calculate it i always get negative infinity.

My calculations are that 1/pi is a meaningless constant leaving us with -cos(x)/sin(x). cos(pi)=-1 and sin(pi)=0 so we have that - (-1) divided by an extremely small (negative, as it comes from -pi) number is equal to infinity. How is that possible? Are there any other ways to argue for the limit is infinity?

Thanks a lot! Any answer will be appreciated!

//DanishKid