Rearrangeing Inverse Hyperbolic functions

[Observables]

Hi,

My brain is not working today. So can someone please tell me what I am doing wrong.

(^2 = squared)

coshy^2 - sinhy^2 = 1, how do I rearrange this for coshy^2

I keep getting: coshy^2 = 1 + Sinhy^2

The book that I'm looking at has it this way: coshy^2 = Sinhy^2 + 1

Thanks

Obs

 

[SteamKing]

Time for brain overhaul. Both expressions evaluate the same.

 

[chiro]

Hi,

My brain is not working today. So can someone please tell me what I am doing wrong.

(^2 = squared)

coshy^2 - sinhy^2 = 1, how do I rearrange this for coshy^2

I keep getting: coshy^2 = 1 + Sinhy^2

The book that I'm looking at has it this way: coshy^2 = Sinhy^2 + 1

Thanks

Obs

Hey observables and welcome to the forums.

The easiest way to find if the book is right (ie coshy^2 - sinhy^2 = 1) is to just use the definition of sinhy and coshy.

sinhy = 1/2 (e^x - e^-x)
coshy = 1/2(e^x + e^-x)

so sinhy^2 = 1/4 [e^2x - 2 + e^-2x)
coshy^2 = 1/4(e^2x + 2 - e^-2x)

coshy^2 - sinhy^2 = 1/2 - (-1/2) = 1

 

[Observables]

Time for brain overhaul. Both expressions evaluate the same.

Hi,

I realized that, but I couldn't figure out how the book was doing the rearranging. I've been differentiating a few Inverse Hyperbolic functions, and I thought the reason that the book rearranged differently to me was that somewhere down the line it would become clear why it was done.

Obs.

 

[Observables]

Hey observables and welcome to the forums.

The easiest way to find if the book is right (ie coshy^2 - sinhy^2 = 1) is to just use the definition of sinhy and coshy.

sinhy = 1/2 (e^x - e^-x)
coshy = 1/2(e^x + e^-x)

so sinhy^2 = 1/4 [e^2x - 2 + e^-2x)
coshy^2 = 1/4(e^2x + 2 - e^-2x)

coshy^2 - sinhy^2 = 1/2 - (-1/2) = 1

Hi Chiro,

Thanks for the info.

Obs.

 

[uart]

Gezzz breakfast time must be confusing at your place. Trying to decide whether to have "eggs and toast" or "toast and eggs". It must keep you occupied for hours.