coth^2 (x) − 1 = csch^2 (x)

Question

I need to prove it by showing work.

Answer 1

The notation in this editor may be a challenge but, here we go:

coth²x -1 = (1/tanh²x) -1 = (1 - tanh²x)/tanh²/x = sech²x/tanh²x = 1/(cosh²x tanh²x) = 1/sinh²x