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. $\frac{5\pi }{4}$
• D. None of these

Answer 1

The correct option is B

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

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

Now, tan(A + B) = $\frac{tanA+tanB}{1-tanAtanB}$ = $\frac{-\frac{1}{2}-\frac{1}{3}}{1-\frac{1}{2}.\frac{1}{3}}$ = -1

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