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Q.
In triangle $A B C, \tan A+\tan B+\tan C=6$ and $\tan A \tan B$ $=2$, then the values of $\tan A, \tan B, \tan C$ are
Trigonometric Functions
Solution:
In a triangle,
$\tan A+\tan B+\tan C=\tan A \tan B \tan C$ ...(i)
$\Rightarrow 6=2 \tan C$
or $\tan C=3$
Also $\tan A+\tan B=6-3=3$ ...(ii)
By Eqs. (i) and (ii), $\tan A$ and $\tan B$ are roots of $x^{2}-3 x+2=0$.
Thus,
$\tan A, \tan B=2,1$ or 1,2 and $\tan C=3$