Hello,

For the first one, apply Ito's lemma to

And you should get

And hence

I must admit I kind of struggled when it came to finding . You know you have to apply Ito's lemma to some transformed , so just try out simple functions of that may cancel out the in the right hand side of the equation.

FYI, this looks like what is called a brownian bridge... (it's in the Wikipedia article)