Firstly, how would someone know what the "best possible answer" is for something that is designed to answer all questions? Secondly when you provide this addit

Firstly, how would someone know what the "best possible answer" is for something that is designed to answer all questions? Secondly when you provide this additional prompt context you are giving the model more to work with including just more information about how you are going to assess the responses. It stands to reason this should give a "better" answer in the sense that it should be able to use that information to give an answer closer to what you are hoping for and it doesn't have to read your mind about what that might be. This is no different from how humans work. For example when you take say a trig exam the question doesn't just say "evaluate tan(3pi/8)" it says something like "Give an exact value for tan(3pi/8) without using a calculator. Simplify where possible and rationalise any denominators but do not remove common factors. Show your working. " The examiner is saying they want to see you know how use the right half angle trig identities etc not just that they can't find their calculator and need you to type something in for them. If they just gave the question in the first form you wouldn't know.