If maximum and minimum values of the determinant
∣ 1 + sin² x cos²x sin 2x ∣
∆X = ∣ sin² x 1+ cos² x sin 2x ∣ are α and β then......
∣ sin² x cos²x 1+ sin 2x ∣

A) α + β⁹⁹ = 4
B) α - β¹⁷ = 26
C) (α²ⁿ - β²ⁿ) is always an even integer for n ∈ N
D) a triangle can be consructed having it's sides as α, β and α - β