Can someone check my work for the following and fix accordingly?

Evaluate the following limits.

1. lim [1-cos^(2) x]/x^2

x->0

2. lim [1-cos2x]/x^2

x->0

3. lim cotx/(pi/2 - x)

x->0

my work:

1. lim (sin^(2)x)/x^2

x->0

i'm stuck here ..

2. lim [sin^2 (x) + cos^2 (x) - cos^ 2(x) + sin^2 (x)]/ x^2

x->0

= lim [2sin^(2) x]x^2

x->0

i'm not sure what step to take next

3. lim [cos (pi/2 - x)]/ [sin (pi/2 -x)]

(pi/2 - x) -> 0

stuck here too..