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  4. The value of the determinant |1&0&0 2& cos x& sin x 3& sin x& cos x| is

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Q. The value of the determinant $\begin{vmatrix}1&0&0\\ 2&\cos x&\sin x\\ 3&\sin x&\cos x\end{vmatrix}$ is

Determinants

Solution:

The value of the given determinant $= 1 (\cos^2 \, x - \sin^2 \, x) = \cos \, 2x$.