Expression involving trig functions not simplifying

I have a complicated function that returns a fairly simple result:

Sqrt[1/Abs[Sec[t/2]]^2 + Sin[t/2]^2]


I can see that this is equal to one, but when I try to simplify it with

Simplify[%, Element[t, Reals]]


nothing happens; it doesn't simplify. What am I doing wrong?

It seems you need ComplexExpand before simplifying, which assumes that all variables are real in its transformation
ComplexExpand[Sqrt[1/Abs[Sec[t/2]]^2 + Sin[t/2]^2]] // Simplify