What is the standard deviation of is #sigma(X)=(sigma(Y))/2#, what is #sigma(X-Y)#?
The standard deviation of a defined continuous function is zero (0).
The standard deviation of a defined continuous function is zero (0) because by its definition each 'x' data point corresponds exactly to each 'y' data point. There is no deviation to measure.
If you meant the difference between the variance and the standard deviation, or the difference between the standard deviation calculated from a sample or a population, you need to review and revise your question.