Question

If tan A = 1/2, tan B = 1/3; then what is the value of tan (2A + B) ?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

Given values are $\tan A=\frac{1}{2}\tan B=\frac{1}{3}\tan \left(2A+B\right)=\frac{\tan 2A+\tan B}{1-\tan 2A\tan B}$
and, $\tan 2A=\frac{2\tan A}{1-{\tan }^{2}A}=\frac{2\frac{1}{2}}{1-\frac{1}{4}}=\frac{4}{3}$
So, $\tan \left(2A+B\right)=\frac{\frac{4}{3}+\frac{1}{3}}{1-\frac{4}{3}\times \frac{1}{3}}=\frac{\frac{5}{3}}{\frac{5}{9}}=3$