I am not sure what you are asking.
But sometimes I get expressions which look like,
And in general there is no way to simplify it, you just leave it like that. Part of the difficulty in the word "simplify" is that it is not well-defined, and hence we cannot come up with a theory which tells us when we can "simplify" and when we cannot. Perhaps you can create a definition.
And, I also do not understand how you got trigonometric functions in your answer. I never remember learning it that.