Need help with a limit in Calculus?

I'm so confused :( I know (sinx)/x as the limit goes to zero is 1.. basic. Today my Calc TA, who has a dubious history of "help" said that limit of (sin(x-2))/(x-2) as x goes to 2 is 1 and if the limit had gone to zero, the answer WOULDN'T be 1. I thought as long as whatever was in the parentheses matched the bottom, the answer would be 1 if x goes to zero. For example, (sin5x)/5x as a limit goes to zero is 1 because of the basic property. Please be absolutely sure before you answer :)