CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If $$A,B$$ and $$C$$ are the angles of non-right angles triangle $$ABC$$, then find the value of $$\begin{vmatrix} \tan { A }  & 1 & 1 \\ 1 & \tan { B }  & 1 \\ 1 & 1 & \tan { C }  \end{vmatrix}$$


Solution

$$A+B=\pi -C$$
$$ \tan { (A+B) } =-\tan { C } $$
$$\displaystyle  \frac { \tan { A } +\tan { B }  }{ 1-\tan { A } \tan { B }  } =-\tan { C } $$
$$ \tan { A } +\tan { B } +\tan { C } =\tan { A } \tan { B } \tan { C } $$     ....(1)
Consider, $$\begin{vmatrix} \tan { A }  & 1 & 1 \\ 1 & \tan { B }  & 1 \\ 1 & 1 & \tan { C }  \end{vmatrix}$$
$$\Delta =\tan { A } \tan { B } \tan { C } -\tan { A } -\tan { C } +1+1-\tan { B } $$
$$\Delta=2$$ (by (1))

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image