# 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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