Question

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

• A. $\pi$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{4}$

Answer 1

Answer: (D)

$\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}=\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}\cdot \frac{1}{3}}=\frac{5/6}{5/6}=1$
$\therefore A+B=45^{\circ }=\frac{\pi }{4}$