Question 1101917
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<pre>
Apply co-factoring the determinant along the first row of the matrix, and you will get


determinant = cos^2(x) - sin^2(x) = cos(2x).
</pre>

About co-factoring determinant see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Co-factoring-a-3x3-determinant.lesson>Co-factoring the determinant of a 3x3 matrix</A> 

in this site.