If we consider only the principal values of the inverse trigonometric function Then the value of $\tan \bigg[\cos ^{-1} \large\frac{1}{5 \sqrt 2} -$$\sin ^{-1} \large\frac{4}{\sqrt{17}}\bigg]$ is

Question

$\begin{array}{1 1} \large\frac{3}{29} \\ \large\frac{2}{5} \\ \large\frac{1}{5} \\ \large\frac{2}{3} \end{array}$