2sin^2(x) sin^2(x) = 2sin^4(x) ;
cos(4x) = 2cos^2(2x) - 1 ....(1)
cos(2x) = 1 - 2sin^2(x) .....(2)
Substituting cos2x from (2) in (1).
We get cos(4x) = 1 + 8sin^4(x) - 8sin^2(x) ;
Thus we get 2sin^4(x) = (cos(4x)-1)/4 + 2sin^2(x) ;
Substituting sin^2(x) from (2) :
2sin^4(x) = [3-4cos(2x)+cos(4x)]/4