Q:  Which expression completes the fundamental trigonometric identity ? sec(-x)

A. -sec x
B. sec x
C. cos x
D. -cos x

A:  This is just a trig identity that should be memorized.  For a list of all of the trig identities, you can go to:

http://en.wikipedia.org/wiki/List_of_trigonometric_identities

Or, you can find them listed on many other websites (or even in your text book probably).

You will find that: sec(-x) = sec(x)

So, the correct answer is B.