b) When you work this out, you'll need to expand cos(2t). Get this in terms of sin^2 t only, then rearrange to get a quadratic in sin(t) that you can solve
c) Follows from b
d) You have y=sin(2t)=2sin(t)cos(t). You can replace cos(t) with x, then use sin^2 t + cos^2 t = 1 to get sin(t) in terms of cos(t), and hence in terms of x. Remember that when you do this, you'll have to consider whether you are taking the positive or genative square root.
e) Similar to the one before, but check again whether you need to use the positive or negative square root.