If your proof is of an identity, then yes, you must use the identity symbol.

If your "proof" is about what happens for one value (or a certain number of values) of a variable ,e.g. "if sin x = 2/3 then prove that cos x = whatever", then it's appropriate to use the equals sign, since your conclusion is not valid for all values of x.

(edited 11 months ago)

Reply 11

mqb2766

Original post by chavvo

If your proof is of an identity, then yes, you must use the identity symbol.
If your "proof" is about what happens for one value (or a certain number of values) of a variable ,e.g. "if sin x = 2/3 then prove that cos x = whatever", then it's appropriate to use the equals sign, since your conclusion is not valid for all values of x.

You may be a bit strong with the "must". For instance, the ms for edexcel 2019 (Q12) uses the equality symbol almost exclusively throughout (apart from the initial question statement)
https://www.mathsgenie.co.uk/alevel/ap2june2019ms.pdf
and there is no mention of losing marks for equality/identity symbol. Similarly the trig identities in the formula sheet use equality etc.

A bit more detailed discussion
https://math.stackexchange.com/questions/1505026/when-do-you-make-use-of-%E2%89%A1-when-verifying-trigonometric-identities
but using equality to represent idenitty is a reasonably common abuse/overloading of common usage (ms and formula sheet and ....) and the "true for all values" is implied. However, using the identity symbol makes it explicit.

(edited 11 months ago)

Reply 12

DFranklin

mqb2766

You may be a bit strong with the "must" [...] the trig identities in the formula sheet use equality etc.

Yes, to me the fact that the list under Trigonometric Identities in the formula booklet uses

=

rather than

\equiv

seems a very strong argument that it's not required.

More generally, as your second link argues: it's extremely rare for post-A-level work to use

\equiv

, arguably this is sloppy, but it is reasonably universal.

Reply 13

chavvo

Original post by mqb2766

You may be a bit strong with the "must". For instance, the ms for edexcel 2019 (Q12) uses the equality symbol almost exclusively throughout (apart from the initial question statement)
https://www.mathsgenie.co.uk/alevel/ap2june2019ms.pdf
and there is no mention of losing marks for equality/identity symbol. Similarly the trig identities in the formula sheet use equality etc.
A bit more detailed discussion
https://math.stackexchange.com/questions/1505026/when-do-you-make-use-of-%E2%89%A1-when-verifying-trigonometric-identities
but using equality to represent idenitty is a reasonably common abuse/overloading of common usage (ms and formula sheet and ....) and the "true for all values" is implied. However, using the identity symbol makes it explicit.

Well, yes, my "must" is more for moral guidance than an absolute directive, but my meaning was really that it's never wrong to get into good habits when proving things, and certainly if I were proving an identity (which should never be more than 3 or 4 lines at A level) then I would make sure (for my own peace of mind if nothing else) that I wrote down the identity symbol throughout - especially in an exam. And I'm the sort of person who still puts QED at the end of proofs rather than a square box!

But then when using an identity (or several such) to simplify an expression e.g. involving lots of trig subs, I really wouldn't bother :smile:

And as someone who doesn't have to worry about exams, I could choose to use whichever suits me on the day! And I could even start whole sentences with "And" or "But", which is something I would never recommend to a student.