Cosh x / sinhx in the form of e^x

[goldfish9776]

Homework Statement

I was told that coshx = (e^x + e^-x) / 2 , why cosh2x = (e^2x - e^-2x) / 2 ?

Homework Equations

The Attempt at a Solution

 

[LCKurtz]

Homework Statement

I was told that coshx = (e^x + e^-x) / 2 , why cosh2x = (e^2x - e^-2x) / 2 ?

Homework Equations

The Attempt at a Solution

Because it is true for any value of x. Any number you can get with x you can get with 2x.

 

[goldfish9776]

If cosh3x then e^x is substituted with e^3x ??

 

[SammyS]

If cosh3x then e^x is substituted with e^3x ??

Yes. Although you really should use parentheses for the expression making up the exponent unless it's written as a superscript.

e^(3x) or e^3x .

 

[Buzz Bloom]

I was told that coshx = (e^x + e^-x) / 2 , why cosh2x = (e^2x - e^-2x) / 2 ?

Hi goldfish9776:

I agree that the minus sign in

cosh 2x = (e^2x - e^-2x) / 2​

is peculiar.

(e^2x - e^-2x) / 2 = sinh 2x.​

Is the person who told you that

cosh 2x = (e^2x - e^-2x) / 2​

someone you would expect to be reliable?

Regards,
Buzz

 

[SammyS]

@goldfish9776 ,

You have a typo in the OP. The correct statement is:

##\displaystyle \cosh(2x)=\frac{e^{2x}+e^{-2x}}{2} ##