Understanding Hyperbolic Functions: A Worked Example from Definitions

[Firepanda]

Cosh u = (2sinh u) -1

Working from definitions

http://img118.imageshack.us/img118/3271/eusm4.png

Its a worked example from the book, which isn't very well explained. The only step i struggle on is from how the managed to get all the u's positive (step 2). I plugged some numbers in for u and find the two equations don't equal each other anyway. What am i doing wrong?

thx

 

[George Jones]

Cosh u = (2sinh u) -1

The only step i struggle on is from how the managed to get all the u's positive (step 2).

What happens when you multiply the second equation in your linked image by e^u?

I plugged some numbers in for u and find the two equations don't equal each other anyway. What am i doing wrong?

Right, this equation isn't satisfied by all values of u. You are supposed to find the values of u for which it is satisfied.

 

[Firepanda]

What happens when you multiply the second equation in your linked image by e^u?



Right, this equation isn't satisfied by all values of u. You are supposed to find the values of u for which it is satisfied.

gotcha thx!