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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Determinants
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If $A,B,C$ are angles of a triangle then $\begin{vmatrix}e^{2iA}&e^{-iC}&e^{-iB}\\e^{-iC}&e^{2iB}&e^{-iA}\\e^{-iB}&e^{-iA}&e^{2iC}\end{vmatrix}$ is equal to


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Since $A+B+C=\pi$ and $e^{i\pi}=\cos \pi+i\sin \pi=-1$
By taking $e^{iA},e^{iB},e^{-ic}$ common from $R_1,R_2$ and $R_3$ respectively ,we have
By taking $e^{iA},e^{iB},e^{iC}$ common from $C_1,C_2$ and $C_3$ respectively we have
Hence (c) is the correct answer.
answered Nov 25, 2013 by sreemathi.v
edited Mar 20, 2014 by sharmaaparna1

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