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

Answer 1

Prove not price.
Prove the hyperbolic function 1-tanh^2x=sech^2x

Answer 2

cosh^2 - sinh^2 = 1
divide by cosh^2 to get
1 - tanh^2 = sech^2

Answer 3

tanh = sinh/cosh
sech = 1/cosh
1 - tanh^2 = 1 - sinh^2/cosh^2
sech^2 = 1/cosh^2
so
does
cosh^2 - sinh^2 = 1 ? Yes

Answer 4

in case you don't believe the basic hyperbolic trig identity
cosh^2 x - sinh^2 x = 1, go back to the definition.

((e^x + e^-x)/2)^2 - ((e^x - e^-x)/2)^2
= (e^2x + 2 + e^-2x)/4 - (e^2x - 2 + e^-2x)/4
= 4/4
= 1