On the first one, I get the same answer you did.
On the second, you could write tanx sinx.
On the third, I think you mean sec^2(x) not cosecant.
On the fourth, again I get the same result you did.
The one about the fourth powers, for which you didn't show an attempt ... it's a difference of two squares, isn't it? And one of the factors will be another difference of squares, right? Does that help?
What are the choices available?