Second Derivative of Parametric Equation

Calculus Level 3

Let \(x,y : \mathbb{R} \to \mathbb{R}\) be functions satisfying \(y(t) = \sin^2 t\) and \(x(t) = \cos t\) for all \(t\). The second derivative \(\frac{d^2 y}{d x^2}\) is a constant function, equal to \(a\) everywhere. Find the value of \(a\).

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