With formula this gets hard

Calculus Level 2

If \(C\) is the curve defined by \(x(t)=\cos^2(t)\) and \(y(t)=\sin^2(t)\). The side length of \(C\) for \(t\in [0,\frac{\pi}{2}]\) is in the form \(\sqrt{a}\). Find the value of \(a\)

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