Correct option (C) π/2
From the second equation, we have
sin2B = 3/2sin2A
and from the first equality
3sin2 A = 1 –2 sin2B = cos2B
Now cos (A + 2B) = cosA⋅cos2B – sinA⋅sin2B
= 3 cosA⋅sin2A - 3/2 ⋅sinA⋅sin2A
= 3cosA⋅sin2A – 3sin2A⋅cosA = 0
⇒ A + 2B = π/2 or 3π/2
Given that 0 < A π/2 and 0 < B < π/2
⇒ 0 < A + 2B < π + π/2
Hence, A + 2B = π/2