2 The curve \(C\) has parametric equations
$$x = \cosh t , \quad y = \sinh t , \quad \text { for } 0 < t \leqslant \frac { 3 } { 5 }$$
The length of \(C\) is denoted by \(s\).
- Show that \(s = \int _ { 0 } ^ { \frac { 3 } { 5 } } \sqrt { \cosh 2 t } \mathrm {~d} t\).
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- By finding the Maclaurin's series for \(\sqrt { \cosh 2 t }\) up to and including the term in \(t ^ { 2 }\) ,deduce an approximation to \(s\) .