# By using properties of determinants ,prove that :$\begin{vmatrix}1+\sin^2x& \cos ^2x&4\sin 2x\\\sin^2x & 1+cos^2 x& 4\sin 2x\\\sin^2 x& \cos ^2x &1+4\sin 2x\end{vmatrix}=2+4\sin 2x$.

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