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problems with sinh^2

don't see the point in making a new thread so i'll just bump this one

this is the end of a question which i'm stuck on

basically i have to make

e^t-2+e^{-t}= 4sinh^{2}(t)

however, I can't work it out for the life of me

when i work backwards i find that

Unparseable latex formula:

sinh^{2}(t))=1/4(e^{2t}-2+e^{-2t}_

, so I can see the similarity, but I don't know how to change it in to that form.
Am I just making a silly mistake again or what?
My answer is fully correct up until this point, but the next line is basically what I've written up at the top and I don't know why. Is it just a rule I'm supposed to know?

basically all I can find is that

e^t-2+e^{-t}=(e^{t/2}-e^{-t/2})^2

so i THINK that means i have

e^t-2+e^{-t}=2(sinh^2(t/2))

close but no cigar...

Reply 1

squeezebox

You've integrated, so remember you need a constant of integration::

\frac{dW}{W} = -(q/p)dx \rightarrow logW = \frac{-p}{q} + log(k)

where logk is just an arbitrary constant. Rearranging this yets you the answer.

Reply 2

munn

ah brilliant thanks
schoolboy error

bump for new problem

You're missing the factor of a half from the exponential form of sinh (t).

Reply 5

munn

hmmm?
whereabouts?
oh yeah, that's just a mistake in typing it up, i have that on my work

Reply 6

Oh I Really Don't Care

munn

hmmm?
whereabouts?
oh yeah, that's just a mistake in typing it up, i have that on my work

You are solving for t.

The above is certainly not an identity [most]

Reply 7

Edenr

Are you sure you have the question correctly?

Reply 8

munn

it's pretty confusing, I have everything correct up until a certain point, basically i have this line:

1/(4(e^t-2+e^-t))

and that's what's in the answers
but the next line is then

=1/(16sinh^2(t))

which is where I'm gettin stuck, as I can't see how they equal each other.

Reply 9

munn

basically, the red arrow is where i'm getting stuck, maybe that'll make it easier to understand what i'm trying to say

Reply 10

yusufu

munn

basically, the red arrow is where i'm getting stuck, maybe that'll make it easier to understand what i'm trying to say

~~I don't see a picture...~~
Now I do.

Reply 11

munn

strange

try clicking this link... http://www.pocketmonkey.co.uk/media/68/Untitled.jpg

Reply 12

yusufu

munn

basically, the red arrow is where i'm getting stuck, maybe that'll make it easier to understand what i'm trying to say

I'm afraid that the working is just not true. sinh^2(t/2), yes, but not sinh^2 t.

Reply 13

munn

that's what I thought, i even double checked the question to see if maybe it was an error in the working (there's been a few) but the question in particular asks you to prove that it can be written as 1/16cosech^2 t, that's what's confused me.
Oh well
thanks anyway, i've spent pretty much the last 2 days trying to work that out to no avail, you've shown me that i'm NOT going crazy anyway

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