Prove the identity (sinh x)^2 = (cosh 2x - 1) / (2)

Question

goformit100 · Answer

is 'h' showing the multiple angle ?

anonymous · Answer

No it is hyperbolic sin x

anonymous · Answer

pretty sure it is 100% algebra using 
$$\sinh(x)=\frac{e^x-e^{-x}}{2}$$

anonymous · Answer

Yes, but have a look at this solution, I don't know where the 1/2 comes from?

larseighner · Answer

The half is factored out.  It "comes" from the 4 in the denominator which is then reduced to two.

anonymous · Answer

Ah, makes sense, but what about the -1? because -2(e^0) = -2 isn't it?

larseighner · Answer

It does equal -2. But (-2/2) = 1.  The half came out of the denominator.  It did not touch the numerator. All of the numerator has the common denominator of 2.  So you pull -2/2 out with simple addition.  (ething -2 + ething)/2 = (ething + ething)/2 - 2/2 = (ething + ething)/2 -1.

anonymous · Answer

Ohh, now I get it, thank you so much for the help :)