A) \[\frac{{{a}^{3}}}{a+b+c}\]
B) \[\frac{{{b}^{3}}}{a+b+c}\]
C) \[\frac{{{c}^{3}}}{a+b+c}\]
D) \[\frac{abc}{a+b+c}\]
Correct Answer: A
Solution :
We have\[\tan \alpha =\frac{a}{x},\,\,\tan \beta =\frac{b}{x}\]and\[\tan \gamma +\frac{c}{x}\] \[\therefore \] \[\alpha +\beta +\gamma ={{180}^{o}}\] So,\[\tan \alpha +\tan \beta +\tan \gamma =\tan \alpha \cdot \tan \beta \cdot \tan \gamma \] or \[\frac{a}{x}+\frac{b}{x}+\frac{c}{x}=\frac{a}{x}\cdot \frac{b}{x}\cdot \frac{c}{x}\] or \[{{x}^{2}}=\frac{abc}{a+b+c}\]You need to login to perform this action.
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