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?
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.