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The value of the determinant $Δ=\begin{vmatrix}cos(\alpha + \beta) & -sin(\alpha + \beta) & cos 2 \beta \\sin \alpha & cos \alpha & sin \beta \\-cos \alpha & sin \alpha & -cos \beta \end{vmatrix},$ is |
$cos^2 \alpha $ $sin^2 \alpha $ $sin ( \alpha - \beta )$ 0 |
0 |
The correct answer is option (4) : 0 Applying $R_1→R_1+(sin \beta ) R_2 + (cos \beta ) R_3 ,$ we get $Δ=\begin{vmatrix}0 & 0 & 0 \\sin \alpha & cos \alpha & sin \beta \\-cos \alpha & sin \alpha & -cos \beta \end{vmatrix}=0$ |
