If $\sin B=\large\frac{1}{5}$$\sin(2A+B)$ then $\large\frac{\tan(A+B)}{\tan A}$ is equal to

Question

$(a)\;\large\frac{5}{3}$$\qquad(b)\;\large\frac{2}{3}$$\qquad(c)\;\large\frac{3}{2}$$\qquad(d)\;\large\frac{3}{5}$