Trigonometry

Geometry Level 3

{asin3x+bcos3x=sinxcosxasinx=bcosx\large \begin{cases} a\sin^3 x +b\cos^3 x =\sin x \cos x \\ a \sin x= b\cos x \end{cases}

aa and bb are non-zero constants such that for some xx, the above equation is satisfied. Find a2+b2a^2+b^2.

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