I'm interested in the square root ones - I would say that they are all false because of the plus or minus, but I'm not sure that's what you are looking for here?
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But at this point I think I should say that we are only having this discussion because it's a really interesting worksheet with lots of things to talk about. I wouldn't want anyone to get the impression that I think it's without merit! I'd make tweaks but that can happen in class Q&A
"an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B produce the same value for all values of the variables within a certain domain of discourse" My view is that some of the mentioned positive square roots are identities.
I agree with @susanwhitehouse.bsky.social that these are not identities. Pedagogically, I think we dig a hole if we let students refer to them as identities based on an unspecified domain. If a student changes \sqrt{x^2} to x, it gets red ink and/or it leads to a wrong result later in the problem.
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(That's a plural "your", by the way)
sinx/n = six = 6.