If \( x=a \cos \theta+b \sin \theta \) and \( y=a \sin \theta-b \cos \theta \), prove that \( x^...

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If \( x=a \cos \theta+b \sin \theta \) and \( y=a \sin \theta-b \cos \theta \), prove that \( x^{2}+y^{2}=a^{2}+b^{2} \).
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