If A and B are acute angles such that 2A + 2B = π, then what is the maximum value of sinA·sinB?
A.1/2✓ Correct
B.1/4
C.√3/4
D.1
Explanation
Given A + B = π/2, so B = π/2 - A, meaning sinB = cosA. Then sinA·sinB = sinA·cosA = (1/2)sin(2A). Maximum value of sin(2A) is 1, so maximum of sinA·sinB = 1/2.
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