This question is best explained by an example. Ignore the mathematical context, it doesn't really matter.
... as x tends to 0, the point P slides towards P', so cos x (and hence 1/cos x) both have a limit equal to 1. ...
Given that parentheses are usually meant as an aside, if I read the text ignoring the parentheses:
... so cos x both have a limit equal to 1 ...
the "both" here is grammatically incorrect (as, of course, cos(x) is a single "thing").
So here comes the question in the title: Do sentences need to remain grammatically correct if text in parentheses are ignored? And as a side question, what would be a better thing to use in the example?
by Nicole Dehé](https://books.google.co.uk/books?id=ejaNAwAAQBAJ&printsec=frontcover&dq=Parentheticals+in+Spoken+English:+The+Syntax-Prosody+Relation+By+Nicole+Deh%C3%A9&hl=en&sa=X&ved=0ahUKEwiav6_9hufLAhVBtBQKHZd3ASYQ6AEIHTAA#v=onepage&q=Parentheticals%20in%20Spoken%20English%3A%20The%20Syntax-Prosody%20Relation%20By%20Nicole%20Deh%C3%A9&f=false) is found ...
– Edwin Ashworth Mar 29 '16 at 23:53Syntactic amalgamation has been analysed in terms of parenthesis: … (1.19) Syntactic amalgamation: (a) John invited you’ll never guess how many people to his party. (Lakoff 1974: 321) / (b) John is going to I think it’s Chicago on Sunday. (Lakoff 1974: 324) >> [the claimed parentheticals in italics]. Obviously, omitting these destroys grammaticality.
– Edwin Ashworth Mar 29 '16 at 23:55