sin^4a+cos^4a=

We have

(sin^2a x sin^2a + cos^2a x cos^2a) =

sin^2a x sin^2a + (1- sin^2a) x (1- sin^2a) =

sin^2a x sin^2a + 1 - 2sin^2a + sin^2a x sin^2a  =

2 sin^4a + 1 - 2 sin^2a =

2sin^4a - 2sin^2a + 1

{Note.....other answers are possible}