Proving the Cosh and Sinh Identity

  • Thread starter Thread starter aaaa202
  • Start date Start date
  • Tags Tags
    Identity
Click For Summary

Homework Help Overview

The discussion revolves around proving an identity involving hyperbolic functions, specifically sinh and cosh, expressed in terms of exponentials. The original poster seeks to validate the equation for an exercise but is uncertain about the approach to take.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants suggest using the definitions of sinh and cosh to rewrite the equation in terms of exponentials. There is also a mention of the identity cosh² + sinh² = 1, which is questioned by some as being incorrect in this context.

Discussion Status

The conversation is ongoing, with participants exploring different interpretations of the hyperbolic identities. Some guidance has been offered regarding the correct relationships between the functions, but no consensus has been reached on the approach to proving the identity.

Contextual Notes

There are indications of confusion regarding the application of hyperbolic identities, particularly the relationship between cosh and sinh. The original poster expresses a need for correctness in their exercise, highlighting the importance of clarity in the definitions used.

aaaa202
Messages
1,144
Reaction score
2
Is it true that:

exp(2x)sinh(y)2 + exp(-2x) = exp(2x)cosh(y)2-2sinh(2x)

I need this to be correct for an exercise but I don't know how to show it. I tried using something like cosh2+sinh2=1, but it didn't work.
 
Physics news on Phys.org
Perhaps use the definition of sinh and cosh to express everything as exponentials?
 
aaaa202 said:
I tried using something like cosh2+sinh2=1, but it didn't work.

In general cosh2+sinh2 ≠1 :wink:
 
aaaa202 said:
Is it true that:

exp(2x)sinh(y)2 + exp(-2x) = exp(2x)cosh(y)2-2sinh(2x)

I need this to be correct for an exercise but I don't know how to show it. I tried using something like cosh2+sinh2=1, but it didn't work.

It might also help if you use the correct relation. cosh^2-sinh^2=1.
 
I thought ;) would propel him there. ;)
 
epenguin said:
I thought ;) would propel him there. ;)

Yeah, I didn't see your hint until after I posted. Sorry.
 
No matter. :smile:
 

Similar threads

Modulus of a complex number with hyperbolic functions
  • · Replies 2 ·
Replies
2
Views
3K
How should I show that ## B ## is given by the solution of this?
  • · Replies 2 ·
Replies
2
Views
1K
Determine whether ## S[y] ## has a maximum or a minimum
  • · Replies 18 ·
Replies
18
Views
3K
Comparing Hyperbolic and Cartesian Trig Properties
  • · Replies 1 ·
Replies
1
Views
2K
Finding Energies For 1D Potential
  • · Replies 20 ·
Replies
20
Views
3K
Solving the Mystery of sinh(-3) ≥ -3 or sinh(-3) ≤ -3?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Principal and Gaussian curvature of the FRW metric
  • · Replies 8 ·
Replies
8
Views
2K
Find the ##r^{th}## term of ##(a+2x)^n##
  • · Replies 3 ·
Replies
3
Views
2K
MHB Solving a complex value equation
  • · Replies 4 ·
Replies
4
Views
2K
Explaining sinh and cosh graphically
  • · Replies 3 ·
Replies
3
Views
2K