Hyperbolics - Use Osborne's Rule to show sech^2x=1-tanh^2x

Im not quite sure what I need to do,

I know

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?

Re: Hyperbolics - Use Osborne's Rule to show sech^2x=1-tanh^2x

Re: Hyperbolics - Use Osborne's Rule to show sech^2x=1-tanh^2x

Quote:

Originally Posted by

**tjnortham** Im not quite sure what I need to do,

I know

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?

Re: Hyperbolics - Use Osborne's Rule to show sech^2x=1-tanh^2x

Quote:

Originally Posted by

**tjnortham** Im not quite sure what I need to do,

I know

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?

I haven't seen Osborne's rule used in any of the previous methods. At least, not directly. You know that

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?