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= (sin²A + cos²A + 2sinAcosA) - (sin²A + cos²A - 2sinAcosA)
= (1 + 2sinAcosA) - (1 - 2sinAcosA)
= 2 sinAcosA + 2 sinAcosA
= sin2A + sin2A
= 2 sin2A