Quantitative Aptitude Ques 1463
Question: If $ \frac{\sin \theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{5}{4}, $ then the value of $ \frac{{{\tan }^{2}}\theta +1}{{{\tan }^{2}}\theta -1} $ is
Options:
A) $ \frac{25}{16} $
B) $ \frac{41}{9} $
C) $ \frac{41}{40} $
D) $ \frac{40}{41} $
Show Answer
Answer:
Correct Answer: C
Solution:
- Given, $ \frac{\sin \theta +cos\theta }{\sin \theta -\cos \theta }=\frac{5}{4} $ On dividing by $ \cos \theta $ in numerator and denominator respectively.
$ \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} $
BETA
