If sin(A + B) = 1 and 2sin(A – B) = 1, where 0 < A < B < π/2, then what is tan A : tan B equal to? - NDA Mathematics 2021 (II)

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If sin(A + B) = 1 and 2sin(A – B) = 1, where 0 < A < B < π/2, then what is tan A : tan B equal to?