Understanding Hyperbolic Functions: Problem & Answer Explained

[hyper]

I have a picture of a problem and the answer. But a place in the answer I can't understand how they get from one function to the next, could you guys please explain it? I have marked it in red?

http://img381.imageshack.us/img381/1839/hyperik2.png

 

[nicksauce]

Well the way they did it was they substituted in for the tanh, using what v is supposed to be. However, I don't necessarily agree with this solution because it starts by assuming the conclusion.

Edit: Actually, I suppose that would be okay, as long as you add a sentence, saying that the solution must be unique.

 

[hyper]

thanks!