\[\left| \begin{matrix} 1+{{\sin }^{2}}\theta & {{\sin }^{2}}\theta & {{\sin }^{2}}\theta \\ {{\cos }^{2}}\theta & 1+{{\cos }^{2}}\theta & {{\cos }^{2}}\theta \\ 4\sin 4\theta & 4\sin 4\theta & 1+4\sin 4\theta \\ \end{matrix} \right|=0\] then \[\sin 4\theta \]equal to [Orissa JEE 2005]

\[\left| \begin{matrix} 1+{{\sin }^{2}}\theta & {{\sin }^{2}}\t

1.	\[\left\| \begin{matrix} 1+{{\sin }^{2}}\theta & {{\sin }^{2}}\theta & {{\sin }^{2}}\theta \\ {{\cos }^{2}}\theta & 1+{{\cos }^{2}}\theta & {{\cos }^{2}}\theta \\ 4\sin 4\theta & 4\sin 4\theta & 1+4\sin 4\theta \\ \end{matrix} \right\|=0\] then \[\sin 4\theta \]equal to [Orissa JEE 2005]
A.	44228
B.	1
C.	-0.5
D.	-1
Answer» D. -1

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\[\left| \begin{matrix} 1+{{\sin }^{2}}\theta & {{\sin }^{2}}\theta & {{\sin }^{2}}\theta \\ {{\cos }^{2}}\theta & 1+{{\cos }^{2}}\theta & {{\cos }^{2}}\theta \\ 4\sin 4\theta & 4\sin 4\theta & 1+4\sin 4\theta \\ \end{matrix} \right|=0\] then \[\sin 4\theta \]equal to [Orissa JEE 2005]

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