Explanation

Since sin⁴α + cos⁴α = 1 − 2sin²αcos²α = 1 − (1/2)sin²2α, the equation becomes 2(1 − (1/2)sin²2α) − 1 = 0, i.e. sin²2α = 1. With α ∈ (0, π/2), sin 2α = 1 gives 2α = π/2, so cos 2α = 0. Thus sin 2α + cos 2α = 1 + 0 = 1, option (b).