Quantitative Aptitude Ques 1977
Question: If $ \sec \theta +\tan \theta =2, $ then what is the value of $ \sec \theta ? $
Options:
A) $ \frac{3}{2} $
B) $ \sqrt{2} $
C) $ \frac{5}{2} $
D) $ \frac{5}{4} $
Show Answer
Answer:
Correct Answer: D
Solution:
- By trigonometric identity, $ {{\sec }^{2}}\theta -{{\tan }^{2}}\theta =1 $
$ \Rightarrow $ $ (\sec \theta +\tan \theta )(\sec \theta -\tan \theta )=1 $
$ \Rightarrow $ $ \sec \theta -tan\theta =\frac{1}{2} $ (i) and given, $ \sec \theta +\tan \theta =2 $ … (ii) On adding Eqs. (i) and (ii), we get $ 2\sec \theta =\frac{1}{2}+2 $
$ \therefore $ $ \sec \theta =\frac{5}{4} $
BETA
