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