To provide scientific evidence regarding the sugar content in peas, the student should use the Benedict's test. This test is specifically designed to detect the presence of reducing sugars, including fructose.
The other tests mentioned, the vinegar test and the iodine test, do not serve for detecting sugar content. The vinegar test is typically used for acidity or to identify organic compounds, while the iodine test is used to detect starch.
Therefore, the most appropriate choice is the Benedict's test.