OrnaVerum
v 6.30.00
28 Jan 2022
updated 28 Jan 2022

Eqn 14c Help

cosh(z) = ½ (ez + e–z)so cosh2(z) = ¼ (e2z + e–2z + 2)
sinh(z) = ½ (ez – e–z)so sinh2(z) = ¼ (e2z + e–2z – 2)

By subtraction, cosh2(z) – sinh2(z) = ¼ (2+2) = 1

Putting z = x/a, cosh2(x/a) – sinh2(x/a) = 1

Thus √ {1 + sinh(x/a)2} = √ {cosh(x/a)2} = cosh(x/a)