A) $ \frac{25}{16} $
B) $ \frac{41}{9} $
C) $ \frac{41}{40} $
D) $ \frac{40}{41} $
Correct Answer: C
$ \Rightarrow $ $ \frac{\frac{\sin \theta }{\cos \theta }+1}{\frac{\sin \theta }{\cos \theta }-1}=\frac{5}{4} $
$ \Rightarrow $ $ \frac{\tan \theta +1}{\tan \theta -1}=\frac{5}{4} $
$ \Rightarrow $ $ 4\tan \theta +4=5\tan \theta -5 $
$ \therefore $ $ \frac{{{\tan }^{2}}\theta +1}{{{\tan }^{2}}\theta -1}=\frac{9^{2}+1}{9^{2}-1}=\frac{82}{80}=\frac{41}{40} $