How can I simplify the following to sec^2(x):

tan(sqrt(x))/(sqrt(x)) + (2sqrt(x)/(2sqrt(x)*cos^2(x)) - tan(sqrt(x))/(sqrt(x))

That simplifies to the sec^2(x), according to a TI 89 calculator, but not sure exactly how.

And then, for:

x/(x^1) - x/(x^2+1)^2, for some odd reason I get x/(x^2+1)^2 when I try to simplify it, but it should be x^3/(x^2+1)^2.

Thanks for your help.