The curve \(C\) has parametric equations
\(x=\cosh t, \quad y=\sinh t, \quad \text { for } 0\lt t \leqslant \frac{3}{5} .\)

The length of \(C\) is denoted by \(s\).
(a) Show that \(s=\int_{0}^{\frac{3}{5}} \sqrt{\cosh 2 t} \mathrm{~d} t\).
(b) By finding the Maclaurin's series for \(\sqrt{\cosh 2 t}\) up to and including the term in \(t^{2}\), deduce an approximation to \(s\).