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 Question Proving hyperbolic identity ( Physics Forums Calculus Beyond )Updated: 2010-07-25 03:50:22 (16)
 Proving hyperbolic identity \equiv1. The problem statement, all variables and given/known data Hi, I've been given a hyperbolic identity to prove: 2. Relevant equations 3. The attempt at a solution I have Cosh(A+B) and - Cosh(A-B) so i can kind of see that there will be two lots of SinhASinhB and the CoshACoshB will cancel, but how do I prove it? I mean how do I know that Thanks :)
 Answers: Proving hyperbolic identity ( Physics Forums Calculus Beyond )
 Proving hyperbolic identity (have a ? ) Warning, warning, thomas49th! Cosh(A?B) = coshAcoshB ? sinhAsinhB (the opposite sign to cos). (this is because, from Euler's formula … cosx = coshix, isinx = sinhix, so i2sinAsinB = sinhAsinhB ) tiny-tim
 Proving hyperbolic identity Errr sorry I don't follow :S. I've only just started hyperbolics today and havn't used an imaginary numbers with them yet? Thanks :) thomas49th
 Proving hyperbolic identity I assume that you have been taught the definitions of these functions: and That is all you need to prove this identity....What are and ? What does that make the LHS of your identity? What are and ? What does that make the RHS of your identity? Can you show that the two expressions are equivalent? If so, then you prove the identity. gabbagabbahey
Proving hyperbolic identity

Hi thomas49th!
 Originally Posted by thomas49th Errr sorry I don't follow :S. I've only just started hyperbolics today and havn't used an imaginary numbers with them yet? Thanks :)
Oops!

In that case, all you need to know is that "hyperbolic" trig functions cosh sinh tanh sech coth and cosech work almost the same as ordinary trig functions (for example, sinh(2x) = 2sinhx coshx), but occasionally you get a + instead of a minus (or vice versa) … I think only when you have two sinh's.

But, to be on the safe side, use gabbagabbahey's method!

tiny-tim

 Proving hyperbolic identity using the identities i got which is equilivlent to cosh2x. but where next? Thanks ;) thomas49th
Proving hyperbolic identity

 Originally Posted by thomas49th using the identities i got which is equilivlent to cosh2x. but where next? Thanks ;)
I think you'd better show me your work

gabbagabbahey

 Proving hyperbolic identity one 2 cancels so you get a half overall. the difference of two squares acts nicely leaving us with: and i was looking back over the notes in class and I saw that we identified cosh2x as that Right? Thanks :) thomas49th
Proving hyperbolic identity

 Originally Posted by thomas49th … and i was looking back over the notes in class and I saw that we identified cosh2x as that Right? Thanks :)
oh i see … you're proving 2 sinhx coshx = sinh 2x (not cosh 2x! … cosh is the positive one )
but what about the original problem, with A and B?

tiny-tim

Proving hyperbolic identity

[quote=thomas49th;1975600]
 but what about the original problem, with A and B? [/qoute]
hahah that's what im asking you!
Not sure where to go now?
Any pointers :)

Thanks :)

thomas49th

 Proving hyperbolic identity Well, if ....then ....so ___? And so ___? gabbagabbahey
 Proving hyperbolic identity I'm almost there? Thanks :) thomas49th
 Proving hyperbolic identity Hmmm... gabbagabbahey
 Proving hyperbolic identity Notice how there is an A+B and A-B from JUST like in cos(A+B) now how do I show that cos(A+B) = thomas49th
Proving hyperbolic identity

 Originally Posted by thomas49th

aren't you missing a couple of terms in that expression?

gabbagabbahey

 Proving hyperbolic identity arrrg it was just starting to look nice: stick I've goto go to bed... knackard sorry. it's almost midnight ere in merry old england i'd read any other message people post on here in the morning. thanks for everything! :) thomas49th
 Proving hyperbolic identity Looks good, except your missing a factor of 1/2, and one of your signs is incorrect..... you should have: You also know the definition of cosh: ....so ___? And __? And so ___? gabbagabbahey
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