Can someone help me with the following questions:

1) [1-cos2x]/[x^2] as x approaches 0

2) [cotx]/[pi/2 - x] as x approaches pi/2

3) [sin]/[x-pi] as x approaches pi

I know that 1-cosx/x^2 is 1/2, but I don't know how this could be used when it's cos2x. I'm not really sure how I could approach the second or third questions. Could I get some advice?