# Cosh x / sinhx in the form of e^x

1. Feb 13, 2016

### goldfish9776

1. The problem statement, all variables and given/known data
I was told that coshx = (e^x + e^-x) / 2 , why cosh2x = (e^2x - e^-2x) / 2 ?

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### 0056.jpg
File size:
36.4 KB
Views:
45
2. Feb 13, 2016

### LCKurtz

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

3. Feb 13, 2016

### goldfish9776

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

4. Feb 13, 2016

### SammyS

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

e^(3x) or e3x .

5. Feb 14, 2016

### Buzz Bloom

Hi goldfish9776:

cosh 2x = (e2x - e-2x) / 2 ​
is peculiar.
(e2x - e-2x) / 2 = sinh 2x.​

Is the person who told you that
cosh 2x = (e2x - e-2x) / 2 ​
someone you would expect to be reliable?

Regards,
Buzz

6. Feb 14, 2016

### SammyS

Staff Emeritus
@goldfish9776 ,

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

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