Question

If $A+B+C=\pi$ and $\angle C$ is obtuse then $tanA$. $tanB$ is $.........$

• A. $>1$
• B. $<1$
• C. $=1$
• D. $\le 1$

Answer 1

The correct option is B $<1$

Since $A+B=\pi -C$ we have
$tan(A+B)=tan(\pi -C)$
$\Rightarrow \frac{tanA+tanB}{1-tanAtanB}=-tanC>0$ $.......\left(i\right)$
$(\because C$ is obtuse angle $\Rightarrow tanC<0)$
Since, $A$ and $B$ are each less than $\frac{\pi }{2}$, it follows that
$tanA+tanB>0$
Hence $\left(i\right)$ will hold if $1-tanAtanB>0$
$\Rightarrow tanAtanB<1$
Hence, option 'B' is correct.