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Recent questions tagged area-of-a-triangle

In a triangle ABC $\begin{vmatrix} a^2& b\sin A & C\sin A\\b\sin A&1&\cos(B-C)\\C\sin A&\cos (B-C) & 1\end{vmatrix}$ equals

asked Apr 22, 2014 by sreemathi.v

1 answer

If $A,B,C$ are angles of a triangle and $\begin{vmatrix} 1&1&1\\1+\sin A&1+\sin B&1+\sin C\\\sin A+\sin ^2A&\sin B+\sin^2B& \sin C+\sin^2C\end{vmatrix}=0$

asked Apr 22, 2014 by sreemathi.v

1 answer

If $A,B,C$ are the angles of a $\Delta$le then the value of the determinant $\small\begin{vmatrix}-1+\cos B&\cos C+\cos B&\cos B\\\cos C+\cos A&-1+\cos A&\cos A\\-1+\cos B&-1+\cos B&-1\end{vmatrix}$ is

asked Nov 25, 2013 by sreemathi.v

1 answer

If $A,B$ and $C$ are the angles of a $\Delta$le then $\begin{vmatrix}\sin 2A&\sin C&\sin B\\\sin C&\sin 2B&\sin A\\\sin B&\sin A&\sin 2C\end{vmatrix}$ = $\lambda\sin A\sin B\sin C$, then $\lambda$ is

asked Nov 25, 2013 by sreemathi.v

1 answer

If $A,B,C$ are angles of a triangle then $\begin{vmatrix}e^{2iA}&e^{-iC}&e^{-iB}\\e^{-iC}&e^{2iB}&e^{-iA}\\e^{-iB}&e^{-iA}&e^{2iC}\end{vmatrix}$ is equal to

asked Nov 25, 2013 by sreemathi.v

1 answer

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