Hi I have been having a problem regards this question. I spent some time trying to sit through it but to no result.
The Question is
arccosech x = log((1+squareroot(1+x^2)) for x>0
log((1-squareroot(1+x^2)) for x<0
Justify the sign of any square roots.
So this is what I did
I assume that y=arccosech(x) thereby cosech(y)=x
1/(sinh(y)) = 1/(1/2*(e^y)-(e^-y))
2/x=e^y - e^-y
this is totally wrong but I do not know how to continue or to handle problem such as this one. Can any one give me a hint and direction about solving this problem?