Im not quite sure what I need to do,
sech^2x = 1/cosh(x)
I know tanhx = sinhx/coshx
I know that in trig 1+tan^2x would be sec^2x
and I know it is 1-tanh^2x because of the (-) in the sinhx
But, I dont know how to put this all together to prove it?
Osborne's rule simply states that you can convert trigonometric identities to hyperbolic identities, except where there is a product of sines, when you have to change the sign. You know that: you reference it in the op.
So, why not just prove and change the signs where appropriate?