Question

If tan A = $\frac{1}{2},tanB=\frac{1}{3}$ then $\tan \left(A+B\right)=$

• A. $0$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

Answer: (B)

$1$

Given $\tan A=\frac{1}{2},\tan B=\frac{1}{3}$

$\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$

$=\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}\times \frac{1}{3}}$

$=\frac{\frac{3+2}{6}}{\frac{6-1}{6}}$

$=\frac{\frac{5}{6}}{\frac{5}{6}}$

$=1$