Final answer:
The question intended to find sin(2A) given sinA + cosA = 3/2 by using the double-angle identity. However, after correctly applying the identity and algebraic manipulation, we obtain a value for sin(2A) that is not possible, suggesting an inconsistency in the given information.
Step-by-step explanation:
The student is asking to find the exact value of sin(2A) given the equation sinA + cosA = 3/2. To find sin(2A), we can use the double-angle formula for sine, which states sin(2A) = 2sinA*cosA. However, we first need to find the individual values of sinA and cosA that satisfy the given equation.
To solve for sinA and cosA, we square both sides of the given equation to get (sinA + cosA)² = (3/2)². Expanding the left side gives sin²A + 2sinA*cosA + cos²A and knowing that sin²A + cos²A = 1, we substitute to get 1 + 2sinA*cosA = 9/4. From here we can solve for sin(2A), which equals 2sinA*cosA. We find that 2sinA*cosA = 9/4 - 1 = 5/4, thus sin(2A) = 5/4.
However, this result cannot be since the sine of an angle cannot be greater than 1. This implies there is an error in the solution or the premise. Therefore, we would need additional constraints to solve this correctly, as the given condition is mathematically inconsistent.