Verified answer

y = cos^4 (x) - 2*cos^2 (x) * sin^2 (x) + sin^4 (x) = (cos^2 (x) - sin^2 (x) ) ^ 2 = { cos^2 x - sin^2 x = cos(2x)} = cos ^2 (2x)

0 ≤ cos^2 (2x)  ≤ 1

E(f) = [0, 1]