A) Equilateral or isosceles
B) Equilateral or right-angled
C) Right angled or isosceles
D) None of these
Correct Answer: A
Solution :
[a] \[\left| \begin{matrix} 1 & \sin A & {{\sin }^{2}}A \\ 1 & \sin B & {{\sin }^{2}}B \\ 1 & \sin C & {{\sin }^{2}}C \\ \end{matrix} \right|=0\] \[\Rightarrow (sinA-sinB)(sinB-sinC)(sinC-sinA)=0\] \[\Rightarrow \sin A=\sin B\,\,or\,\,\sin B=\sin C\,\,or\,\,\sin C=\sin A\] \[\therefore \] at least two of A, B, C are equal. Hence the triangle is isosceles or equilateral.You need to login to perform this action.
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