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

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The function cosh(2x) + 2sinh^2(x) needs to be expressed in terms of exponential functions. Initial attempts to simplify the expression included incorrect algebra, particularly in handling the term 2sinh^2(x). The correct expression for sinh^2(x) is 1/2(e^x - e^(-x))^2, which should be expanded using the FOIL method rather than simply squared. A consensus emerged that the factor of 1/2 cancels out with the 2 in front of sinh^2(x), leading to confusion about the final simplification. Clarification on these algebraic steps is essential for accurate results.
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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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