How does cooking food changes its content of carbohydrates and sugar?
This is a rather general question, and I will try to answer it in a general manner. 

First, the total amount of carbohydrates will not change, or maybe there will be a neglible reduction due to things like burning tiny bits of surface carbohydrates to carbon, or cleaning the vegetables. 

Second, the ratio of all carbohydrates to everything else can easily change, due to evaporation. So if you start with a vegetable that is 10% carbohydrates and 90% water, you can end up with one that is 30% carbohydrates and 70% water, rounded (the numbers I am using are pretty arbitrary, the real range is very large). It is easy to find out the direction of change yourself (the carbohydrate density will go up if you evaporate water, and down if you add water), but calculating the actual amount can be a pain. You'd have to know the initial density to start with, and then monitor the initial and final weight of the food. 

Third, the ratio of sugar to nonsugar carbohydrates can change. It will always go from more complex to less complex carbohydrates - from polysaccharides to oligosaccharides to monosaccharides. So you can sometimes produce conditions under which starch turns into glucose, or sucrose turns into glucose+fructose, although this won't happen every time you cook. I cannot think of any cooking process that will convert sugars in the other direction. The magnitude of that conversion will vary wildly in practice, depending on the very specific chemical conditions in your cooking pot. 

Fourth, there is another effect, but it is likely to be very small in magnitude. The browning of food happens during the Maillard reaction, which is a family of reactions between a carbohydrate and an amino acid. While it is best known from meat, where I think it involves mostly glycoproteins from the animal cells themselves, vegetables brown too, and I suppose some carbohydrates from the vegetables "disappear" in this kind of reaction. It is a thing that happens mostly on the surface of roasted food, and in a specific temperature range, so while it contributes a lot to the aroma, I don't think it actually converts much carbohydrates away.