Question

I need help with proof
So it's 2sinh^2 x+1 = cosh(2x)
So what I did is Lhs= 2times (e^x -e^-x/2) ^2 +1
From which I am getting
(e^2x - e^-2x +2)/2
For a right answer I need this to be (e^2x +e^-2x)/ 2
Which I dunno how to get rid of +2 and make the operator positive ?

Answer 1

\[\cosh(2x) = \frac{ 1 }{ 2 }(e^{-2x}+e^{2x})\] and \[2\sinh^2(x) = 2(\frac{ 1 }{ 2 }(-e^{-x}+e^x))^2\] right

Answer 2

Yes