the relation between tanh and sech

Question

u=(tanhx/1+sechx)

Answer 1

cosh²(x)-sinh²(x)=1, so, dividing through by cosh²(x):

1-tanh²(x)=sech²(x) is the relationship between sech(x) and tanh(x).

Therefore tanh²(x)=1-sech²(x), and tanh(x)=√(1-sech²(x)).

Alternatively sech(x)=√(1-tanh²(x)).

u=tanh(x)/(1+sech(x))=sinh(x)/[cosh(x)(1+sech(x))=sinh(x)/(cosh(x)+1).