If sin⁴α + 4cos⁴β + 2 = 4√2sinαcosβ; α, β ∈ [0, π], then cos(α + β) - cos(α - β) is equal to:

The correct option is B -√2
A.M. ≥ G.M.
sin⁴α + 4cos⁴β + 1 + 1 ≥ 4(sin⁴α ⋅ 4 ⋅ cos⁴β ⋅ 1 ⋅ 1)^(1/4)
⇒ A.M. = G.M. ⇒ sin⁴α = 1 = 4cos⁴β
sinα = ±1, cosβ = ±1/√2
sinβ = 1/√2 as β ∈ [0, π]
cos(α + β) - cos(α - β) = -2sinαsinβ = -√2