Question

If A, B, C are the angles of a triangle, show that $\tan A+\tan B+\tan C=\tan A\tan B\tan C$.

Answer 1

$\because \tan (A+B+C)=\tan \pi =0$,
$\therefore \frac{S_1-S_3}{1-S_2}=0$ or $S_1=S_3$ ..$\left(1\right)$
or $\tan A+\tan B+\tan C=\tan A\tan B\tan C$.