Question

If $A=35^{\circ}, B=15^{\circ}$ and $C=40^{\circ}$, then $\tan A \cdot \tan B+\tan B \cdot \tan C+\tan C \cdot \tan A$ is equal to

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (B)

Given that, $A=35^{\circ}, B=15^{\circ}$ and $C=40^{\circ}$
$\therefore \tan (A+B+C)$
$=\frac{[\tan A+\tan B+\tan C -\tan A \tan B \tan C]}{[1-\tan A \tan B-\tan B \tan C -\tan C \tan A]}$
$\Rightarrow \tan \left(90^{\circ}\right)$
$=\frac{\tan A+\tan B+\tan C-\tan A \tan B \tan C}{1-\tan A \tan B-\tan B \tan C-\tan C \tan A}$
$\Rightarrow \tan A \tan B+\tan B \tan C +\tan C \tan A=1$