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  4. In a triangle ABC if |1 sin A sin 2 A 1 sin B sin 2 B 1 sin C sin 2 C|=0, the triangle must be

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Q. In a triangle $ABC$ if $\begin{vmatrix}1 & \sin A & \sin ^{2} A \\ 1 & \sin B & \sin ^{2} B \\ 1 & \sin C & \sin ^{2} C\end{vmatrix}=0$, the triangle must be

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Solution:

The given equation is $(\sin A-\sin B)(\sin B-\sin C)(\sin C-\sin A)=0$
Therefore either $A=B$ or $B=C$ or $C=A$
$ \Rightarrow a=b$ or $b=c$ or $c=a$.