If tan A = $$\frac{1}{3}\ $$and tan B = $$\frac{2}{5}$$, then what is the value of tan (2A + B) ?

Given : $$tanA=\frac{1}{3}$$ and $$tanB=\frac{2}{5}$$

=> $$tan2A=\frac{2tanA}{1-tan^2A}$$

=> $$tan2A=\frac{2\times\frac{1}{3}}{1-(\frac{1}{3})^2}$$

=> $$tan2A=\frac{\frac{2}{3}}{\frac{8}{9}}$$

=> $$tan2A=\frac{2}{3}\times\frac{9}{8}=\frac{3}{4}$$

To find : $$tan(2A+B)$$

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

= $$\frac{\frac{3}{4}+\frac{2}{5}}{1-(\frac{3}{4})(\frac{2}{5})}$$

= $$\frac{\frac{(15+8)}{20}}{1-\frac{3}{10}}$$

= $$\frac{23}{20}\times\frac{10}{7}$$

= $$\frac{23}{14}$$

=> Ans - (D)