Trigonometry

Geometry Level 3

\[\large \begin{cases} a\sin^3 x +b\cos^3 x =\sin x \cos x \\ a \sin x= b\cos x \end{cases} \]

\(a\) and \(b\) are non-zero constants such that for some \(x\), the above equation is satisfied. Find \(a^2+b^2\).

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