L.H.S = \(\begin{vmatrix} 1+sin^ 2x & cos^2x & 4\,sin\,2x \\ sin^2x & 1+cos^2x & 4\,sin\,2x \\ sin^2x & cos^2x & 1+4\,sin\,2x \end{vmatrix}\)
Applying C1 → C2,
![](https://www.sarthaks.com/?qa=blob&qa_blobid=7586696489269268257)
Applying R2 → R2 - R1, R3 → R3 - R1 ,
![](https://www.sarthaks.com/?qa=blob&qa_blobid=12808288504545339085)
= 2(1 - 0) - 1 (0 - 4 sin 2x)
= 2 + 4 sin 2x = R.H.S