Sin4x - cos⁴x = -sin⁴x
sin4x = -sin⁴x + cos⁴x
sin4x = (cos²x - sin²x)(cos²x + sin²x)
sin4x = cos²x - sin²x
2sin2xcos2x = cos2x
2sin2xcos2x - cos2x = 0
cos2x(2sin2x - 1) = 0
cos2x = 0
2x = π/2 + 2πn, n ∈ Z
x = π/4 + πn, n ∈ Z
2sin2x = 1
sin2x = 1/2
2x = (-1)ⁿπ/6 + πn, n ∈ Z
x = (-1)ⁿπ/12 + πn/2, n ∈ Z
Ответ: x = π/4 + πn, n ∈ Z; (-1)ⁿπ/12 + πn/2, n ∈ Z.