SATHEE: Quantitative Aptitude Ques 686

Quantitative Aptitude Ques 686

Question: If $ \sec \theta +\tan \theta =2+\sqrt{3}, $ then the value of $ \sec \theta $ is

Options:

A) $ \sqrt{3} $

B) $ 2 $

C) $ 4 $

D) $ 2\sqrt{3} $

Show Answer

Answer:

Correct Answer: B

Solution:

$ \sec \theta +\tan \theta =2+\sqrt{3} $ On squaring both sides, we get $ {{\sec }^{2}}\theta +{{\tan }^{2}}\theta +2\sec \theta \tan \theta =4+3+4\sqrt{3} $

$ \Rightarrow $ $ {{\sec }^{2}}\theta +{{\sec }^{2}}\theta -1+2\sec \theta \tan \theta =7+4\sqrt{3} $

$ \Rightarrow $ $ 2{{\sec }^{2}}\theta +2\sec \theta \tan \theta =8+4\sqrt{3} $

$ \Rightarrow $ $ 2\sec \theta (\sec \theta +\tan \theta )=4(2+\sqrt{3)} $

$ \therefore $ $ \sec \theta =\frac{2(2+\sqrt{3})}{\sec \theta +\tan \theta }=\frac{2(2+\sqrt{3})}{(2+\sqrt{3})}=2 $

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