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STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
Question
If $A, B, C$ are the angles of triangle then the value of determinant $\left| {\begin{array}{*{20}{c}}
  {\sin \,2A}&{\sin \,C}&{\sin \,B} \\ 
  {\sin \,C}&{\sin \,2B}&{\sin A} \\ 
  {\sin \,B}&{\sin \,A}&{\sin \,2C} 
\end{array}} \right|$ is
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Answer

b
$\left|\begin{array}{ccc}{\sin A} & {\cos A} & {0} \\ {\sin B} & {\cos B} & {0} \\ {\sin C} & {\cos C} & {0}\end{array}\right| \times\left|\begin{array}{ccc}{\cos A} & {\sin A} & {0} \\ {\cos B} & {\sin B} & {0} \\ {\cos C} & {\sin C} & {0}\end{array}\right|=0$

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