Original post by just.len
Need help in understanding how to prove and solve identities
In trig at A level?
Original post by Muttley79
In trig at A level?
Yes, please
Original post by just.len
Yes, please
https://www.drfrost.org/explorer.php?noid=97 Scroll down
Choose your board on this website: https://mmerevise.co.uk/a-level-maths-revision/
Original post by just.len
Need help in understanding how to prove and solve identities
https://www.tuitionmath.com/single-post/2016/12/09/11-tips-to-conquer-trigonometry-proving
is decent
Original post by Muttley79
The more questions you do the better you will get at it.
https://www.drfrost.org/explorer.php?noid=97 Scroll down
Choose your board on this website: https://mmerevise.co.uk/a-level-maths-revision/
https://www.drfrost.org/explorer.php?noid=97 Scroll down
Choose your board on this website: https://mmerevise.co.uk/a-level-maths-revision/
Thank you for your help.
Thank you for your help.
Really? It does not use the idenitity symbol it uses = at every step.
The last point is terrible - I would not advise this resource at all.
Original post by just.len
Thank you for your help.
Do use the correct smbol between lines - not an = sign.
Do you have to use identity symbol for trig proofs? I never realised that - I always have just used =.
My teachers must have been lenient.
My teachers must have been lenient.
Original post by mosaurlodon
Do you have to use identity symbol for trig proofs? I never realised that - I always have just used =.
My teachers must have been lenient.
My teachers must have been lenient.
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 1 month ago)
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.
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 1 month ago)
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 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 , arguably this is sloppy, but it is reasonably universal.
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.
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
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.Quick Reply
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