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)