Cosh2x+2sinh^2x, not sure if this goes in this forum

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Homework Help Overview

The discussion revolves around expressing the function cosh(2x) + 2sinh²(x) in terms of exponential functions. Participants are exploring the algebraic manipulation of hyperbolic functions.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to express the given function using exponential forms and are questioning the correctness of their algebraic steps. There is a focus on simplifying the expression and understanding the implications of squaring terms.

Discussion Status

There is an ongoing examination of the algebra involved in the transformation of the hyperbolic functions. Some participants have identified potential errors in each other's reasoning, while others are seeking clarification on specific steps in their calculations.

Contextual Notes

Participants are discussing the implications of the squared term in sinh²(x) and how it affects the overall expression. There is uncertainty regarding the application of algebraic identities and simplifications.

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Homework Statement



Express the function cosh(2x)+2 sinh^2(x)= in terms of exponential functions.

Homework Equations


The Attempt at a Solution


i have an answer but I am not sure if its right can someone check please.
=1/2 (e^2x+e^(-2x) )+1/2(e^2x-e^(-2x)) if this is right i need some help simplifying.
 
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No, it's not right. Check your algebra.
 
almost certain that the problem is the 2sinh^2(x), i got 1/2(e^x-e^(-x))^2 which my 89 says is right, then i try to simplify to 1/2(e^(2x)-e^-(2x)) which it says is wrong but i can't see why?
 
If you're trying to say (a+b)2 = a2+b2, that's the reason why. It's not true. You need to FOIL it out. Also, the 1/2 shouldn't be there because it cancels with the 2 in front.
 
thanks i agree with one problem you found but i think that the 1/2 should still be there because its squared in sinh^2 (the 2 isnt) giving 1/4 which then becomes 1/2?? not positive though??
 
Oops, you're right. Sorry.
 

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