Proving the Cosh and Sinh Identity

[aaaa202]

Is it true that:

exp(2x)sinh(y)² + exp(-2x) = exp(2x)cosh(y)²-2sinh(2x)

I need this to be correct for an exercise but I don't know how to show it. I tried using something like cosh²+sinh²=1, but it didn't work.

 

[micromass]

Perhaps use the definition of sinh and cosh to express everything as exponentials?

 

[epenguin]

I tried using something like cosh²+sinh²=1, but it didn't work.

In general cosh²+sinh² ≠1

 

[Dick]

Is it true that:

exp(2x)sinh(y)² + exp(-2x) = exp(2x)cosh(y)²-2sinh(2x)

I need this to be correct for an exercise but I don't know how to show it. I tried using something like cosh²+sinh²=1, but it didn't work.

It might also help if you use the correct relation. cosh^2-sinh^2=1.

 

[epenguin]

I thought ;) would propel him there. ;)

 

[Dick]

I thought ;) would propel him there. ;)

Yeah, I didn't see your hint until after I posted. Sorry.

 

[epenguin]

No matter.