Quantitative Aptitude Ques 1084
Question: If $ \cot \theta =\frac{8}{15}, $ what is the value of $ \sqrt{\frac{1-\cos \theta }{1+\cos \theta }}, $ where $ \theta $ is a positive acute angle?
Options:
A) $ \frac{1}{5} $
B) $ \frac{2}{5} $
C) $ \frac{3}{5} $
D) $ \frac{4}{5} $
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ \cot \theta =\frac{8}{15}=\frac{Base}{Perpendicular} $
$ \therefore $ $ AC=\sqrt{15^{2}+8^{2}} $ $ =\sqrt{225+64}=\sqrt{289}=17 $
$ \therefore $ $ \sqrt{\frac{1-\cos \theta }{1+\cos \theta }}=\sqrt{\frac{1-\frac{8}{17}}{1+\frac{8}{17}}} $ $ =\sqrt{\frac{\frac{9}{17}}{\frac{25}{17}}}=\sqrt{\frac{9}{15}}=\frac{3}{5} $
BETA
