A) 4
B) 1
C) 2
D) 3
Correct Answer: C
Solution :
\[\left| \begin{matrix} \cos x & \sin x & \sin x \\ \sin x & \cos x & \sin x \\ \sin x & \sin x & \cos x \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[{{\cos }^{3}}x+{{\sin }^{3}}x+{{\sin }^{3}}x-3{{\sin }^{2}}x\cos x=0\] \[\Rightarrow \]\[(\cos x+\sin x+\sin x)({{\cos }^{2}}x+{{\sin }^{2}}x+{{\sin }^{2}}\]\[x-\cos x\sin x-\cos x\sin x-{{\sin }^{2}}x)=0\] \[\Rightarrow \]\[\cos x=-2\sin x\]or\[\cos x=\sin x\] \[\tan x=-\frac{1}{2}\]\[\tan =1\Rightarrow x=\pi /4\] \[x=-{{\tan }^{-1}}\frac{1}{2}\] two solutions
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