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$If x^{2} + y^{2} = 1 then {(3 x - 4 x^{3})}^{2} + {(3 y - 4 y^{3})}^{2} =$

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Detailed Solution

$\begin{array}{l} x^{2} + y^{2} = 1 \Rightarrow x = \cos θ, y = \sin θ \\ {(3 x - 4 x^{3})}^{2} + {(3 y - 4 y^{3})}^{2} = {(4 x^{3} - 3 x)}^{2} + {(3 y - 4 y^{3})}^{2} = \cos^{2} 3 θ + \sin^{2} 3 θ = 1 \end{array}$

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