Question

Verify the hyperbolic function
1 - tanh^2x = sech^2x

Answer 1

if you believe cosh^2x - sinh^2x = 1 then just divide through by cosh^2x

If not, then you can verify by using the definitions of
coshx = (e^x + e^-x)/2
sinhx = (e^x - e^-x)/2