Prove the given identity and, where appropriate, check the identity independently by Osborn’s rule.

tanh^2 A + sech^2 A ≡ 1

By which way I can solve this?

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- Mar 10th 2008, 03:20 AMgetonHyperbolic function
Prove the given identity and, where appropriate, check the identity independently by Osborn’s rule.

**tanh^2 A + sech^2 A ≡ 1**

By which way I can solve this? - Mar 10th 2008, 03:39 AMmr fantastic
Substitute the definitions of tanh A and sech A:

Now start simplifying.

As for the check, are you allowed to assume the identity ? I'd say the answer is YES since you're allowed to use Osborne's Rule. Then the check follows easily. - Mar 10th 2008, 09:27 AMSoroban
Hello, geton!

Are we allowed to use__basic__hyperbolic identities?

Quote:

Prove: .

We have: .