If A, B, and C are the angles of a triangle and \[\left| \begin{matrix} 1 & 1 & 1 \\ 1+\sin A & 1+\sin B & 1+\sin C \\ \sin A+{{\sin }^{2}}A & \sin B+{{\sin }^{2}}B & \sin C+{{\sin }^{2}}C \\ \end{matrix} \right|=0,\]then the triangle must be

If A, B, and C are the angles of a triangle and \[\left| \begin{matrix

1.	If A, B, and C are the angles of a triangle and \[\left\| \begin{matrix} 1 & 1 & 1 \\ 1+\sin A & 1+\sin B & 1+\sin C \\ \sin A+{{\sin }^{2}}A & \sin B+{{\sin }^{2}}B & \sin C+{{\sin }^{2}}C \\ \end{matrix} \right\|=0,\]then the triangle must be
A.	Isosceles
B.	Equilateral
C.	Right-angled
D.	None of these
Answer» B. Equilateral

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If A, B, and C are the angles of a triangle and \[\left| \begin{matrix} 1 & 1 & 1 \\ 1+\sin A & 1+\sin B & 1+\sin C \\ \sin A+{{\sin }^{2}}A & \sin B+{{\sin }^{2}}B & \sin C+{{\sin }^{2}}C \\ \end{matrix} \right|=0,\]then the triangle must be

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