Question

In triangle $ABC,\tan A+\tan B+\tan C=6$ and $\tan A\tan B$ $=2$, then the values of $\tan A,\tan B,\tan C$ are

• A. 1,2,3
• B. 3,2/3,7/3
• C. 4,1 /2,3/2
• D. none of these

Answer 1

Answer: (A)

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 $x^2-3x+2=0$.
Thus,
$\tan A,\tan B=2,1$ or 1,2 and $\tan C=3$