SATHEE: Quantitative Aptitude Ques 215

Quantitative Aptitude Ques 215

Question: If $ 0\le \theta \le \frac{\pi }{2} $ and $ {{\sec }^{2}}\theta +{{\tan }^{2}}\theta =7, $ then $ \theta $ is

Options:

A) $ \frac{5\pi }{12} $

B) $ \frac{\pi }{3} $

C) $ \frac{\pi }{5} $

D) $ \frac{\pi }{6} $

Show Answer

Answer:

Correct Answer: B

Solution:

Given, $ {{\sec }^{2}}\theta +{{\tan }^{2}}\theta =7 $

$ \Rightarrow $ $ 1+{{\tan }^{2}}\theta +{{\tan }^{2}}\theta =7 $ $ [\because {{\sec }^{2}}\theta =1+{{\tan }^{2}}\theta ] $

$ \Rightarrow $ $ 1+2{{\tan }^{2}}\theta =7 $

$ \Rightarrow $ $ 2{{\tan }^{2}}\theta =6 $
$ \Rightarrow $ $ {{\tan }^{2}}\theta =3 $

$ \therefore $ $ \tan \theta =\pm ,\sqrt{3} $ Since, $ 0\le \theta \le \frac{\pi }{2} $

$ \therefore $ $ \tan \theta =\sqrt{3} $ $ \theta =60{}^\circ =\frac{\pi }{3} $ [as $ \pi =180{}^\circ $ ]

Quantitative Aptitude Ques 214

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