Question

If $\tan A=-\frac{1}{2}$ and $\tan B=-\frac{1}{3}$,
then $A+B=$

[IIT 1967; MNR 1987; MP PET 1989]

• A. $\frac{\pi }{4}$
• B. $\frac{3\pi }{4}$
• C. None of these
• D. $\frac{5\pi }{4}$

Answer 1

The correct option is B

$\frac{3\pi }{4}$

We have
$\tan A=-\frac{1}{2}$ and $\tan B=-\frac{1}{3}$

$\Rightarrow \tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$
$\Rightarrow \tan (A+B)=\frac{-\frac{1}{2}-\frac{1}{3}}{1-\frac{1}{2}.\frac{1}{3}}\Rightarrow \tan (A+B)=-1$

$\Rightarrow \tan (A+B)=\tan \frac{3\pi }{4}$

$\Rightarrow A+B=\frac{3\pi }{4}$.

Hence the correct answer is Option B