7 The variables \(x\) and \(t\) are related by the differential equation
$$\mathrm { e } ^ { 2 t } \frac { \mathrm {~d} x } { \mathrm {~d} t } = \cos ^ { 2 } x$$
where \(t \geqslant 0\). When \(t = 0 , x = 0\).
- Solve the differential equation, obtaining an expression for \(x\) in terms of \(t\).
- State what happens to the value of \(x\) when \(t\) becomes very large.
- Explain why \(x\) increases as \(t\) increases.