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= (sin^2x + cos^2x)(sin^2x - cos^2x) + 2cos^2x= (1)(1 - 2cos^2x) + 2cos^2x= 1 - 2cos^2x + 2cos^2x= 1
Therefore, the simplified expression is 1.
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
= (sin^2x + cos^2x)(sin^2x - cos^2x) + 2cos^2x
= (1)(1 - 2cos^2x) + 2cos^2x
= 1 - 2cos^2x + 2cos^2x
= 1
Therefore, the simplified expression is 1.