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# Show "this = that" identity proofs watch

1. Hi

I've been revising trig identities for C3 in the realm of:

Show that...

[1-cos(2x)]
----------- = [sec(x)]^2 - 1
[1+cos(2x)]

( by the way, I don't need this solving, thanks! )

I often try working through one side, seeing how far I get to. If I get stuck, I try and work backwards from the other identity, seeing if the 2 can meet in the middle.

Is this a sufficient PROOF for this level (C3) or does there need to be one continuous line of thought? i.e. once I've worked it out do I need to write it up again or otherwise re-order my workings?

Thanks -- I would ask my teacher a boring question like this but it is tomorrow
2. no what you do is fine.

when i had to do proofs i would literally split the page in two. work with one side of the equation on the left as far as i could go, or until i thought it was at a sensible point. then work with the other side of the equation on the right hand side. and keep moving back and forward between them until i got to the answer
3. Showing that a = c, and then that b = c is sufficient to prove that a = b, yes.
4. this = that

-->

is = at.

-->

"He is at university" = "He (at)^2 university"

hmmm

Anyway no don't worry you can work through both sides until they're equal, if you prefer. It is fine as long as the it is clear what is going on, and there are no errors in working.
5. It would be better to start LHS=expression 1=...=expression 2=RHS in one continuous logical argument (for one thing, it's easier to make mistakes doing it the other way round). However, what you describe is valid as a proof (if less elegant), and at C3 level, it's unlikely to make a difference.
6. Thanks all,

[and elegant is an attribute that doesn't apply to me ]
7. Surely if you get half way with the LHS and then work backwards from the RHS until the halfway point you reached before than that is one continuous thought even if you have to copy it out again ?
8. LHS = .... = ... = RHS or RHS = ... = .... = ... = LHS is the best way of doing it. Experience helps you decide the best side to pick but it's usually best to pick the side with either double angles, or lots of secs/cosecs/cots on it.

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Updated: January 19, 2010
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