In a right angled triangle $ABC$, and if $\angle C$ is $90^{\circ}$, and if $\tan B=\large\frac{4}{3}$, find the value of $\sin ^2A+\cos ^2B$

Question

$\begin{array}{1 1} (a)\;\large\frac{9}{25} \\ (b)\;1 \\(c)\;\large\frac{18}{25} \\ (d) \;none\;of\;the\;above\end{array}$