Equivalence of Definitions of Real Area Hyperbolic Secant

Definition 2 implies Definition 1
Therefore:

Also see

 * Equivalence of Definitions of Real Area Hyperbolic Sine
 * Equivalence of Definitions of Real Area Hyperbolic Cosine
 * Equivalence of Definitions of Real Area Hyperbolic Tangent
 * Equivalence of Definitions of Real Area Hyperbolic Cotangent
 * Equivalence of Definitions of Real Area Hyperbolic Cosecant