Do sentences need to remain grammaticaly correct if text in parentheses is ignored? [duplicate]

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?

Solution 1:

Wikipedia states: "Parentheses (singular, parenthesis) (also called simply brackets, or round brackets, curved brackets, oval brackets, or, colloquially, parens) contain material that serves to clarify, or is aside from the main point."

This suggests that the sentence should be read as if the text in parentheses were not there, and as you indicate, "both" is grammatically incorrect in this particular case.

Since the information in parentheses seems to be more than a mere aside, I would have written it differently, removing the parentheses:

so cos x, and hence 1/cos x, both have a limit equal to 1

although a better formulation (less awkward) would be

so both cos x, and hence 1/cos x, have a limit equal to 1

But that's my take. Others may differ.