Question

If $A={35}^0$ , $B={15}^0$ and $C={40}^0$, then the value of $\tan A\tan B+\tan B\tan C+\tan C\tan A$ is equal to

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is B $1$

Given $A={35}^0$ , $B={15}^0$ and $C={40}^0$,

$\tan (A+B+C)=\tan \left(\frac{\pi }{2}\right)=\infty$

We know that $\tan (A+B+C)=\frac{\tan A+\tan B+\tan C-\tan A\tan B\tan C}{1-\tan A\tan B-\tan B\tan C-\tan C\tan A}$

$\Rightarrow$ denominator $=0$

$\therefore \tan A\tan B+\tan B\tan C+\tan C\tan A=1$