The value of $x$ where $d>0$ and $\tan[\sec^{-1}\big(\large\frac{1}{x}\big)]=$$\sin(\tan^{-1}2)$ is

Question

$(a)\;\sqrt 5\qquad(b)\;\large\frac{\sqrt 5}{3}$$\qquad(c)\;1\qquad(d)\;\large\frac{2}{3}$