The expression can be simplified using the identities sin^2x = 1 - cos^2x and cos^2x = 1 - sin^2x.

Thus, we have:
sin^4x - cos^4x + 2cos^2x
= $si{n}^{2}x+co{s}^{2}x$$si{n}^{2}x-co{s}^{2}x$ + 2cos^2x
= $1$$1-2co{s}^{2}x$ + 2cos^2x
= 1 - 2cos^2x + 2cos^2x
= 1

Therefore, the simplified expression is 1.