Hyperbolic Function

demon8991 · 31 Oct 2006 at 13:34

What is cosh(2x) written exponentially?

grahamjenks · 31 Oct 2006 at 13:48

I think its (e^2x+e^-2x)/2

demon8991 · 31 Oct 2006 at 14:18

Yer im trying to construct a proof, just need to maek sure both sides equal each other, i know im close just need to know for sure what cosh(2X) is.

grahamjenks · 31 Oct 2006 at 14:32

Well a long winded way of showing this is:

cosh(x) = (e^x + e^-x)/2

cosh(2x) = 1 + 2sinh(^2)x

sinh(x) = (e^x - e^-x)/2

cosh(2x) = 1 + 2((e^x - e^-x)/2)^2

cosh(2x) = 1+ 2 ((e(2x) - 2 + e(-2x))/4)

cosh(2x) = (e(2x) + e(-2x))/2

demon8991 · 31 Oct 2006 at 14:44

Ahhh brilliant thats what i hoped it would be, thanks mate.

Proof has worked!!!