Quantitative Aptitude Ques 687

Question: For any real value of $ \theta , $ $ \sqrt{\frac{\sec \theta -1}{\sec \theta +1}} $ is equal to

Options:

A) $ \cot \theta -cosec\theta $

B) $ \sec \theta -\tan \theta $

C) $ cosec\theta -\cot \theta $

D) $ \tan \theta -\sec \theta $

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ \sqrt{\frac{\sec \theta -1}{\sec \theta +1}}=\sqrt{\frac{(\sec \theta -1)(sec\theta -1)}{(\sec \theta +1)(\sec \theta -1)}} $ $ =\sqrt{\frac{{{(\sec \theta -1)}^{2}}}{{{\sec }^{2}}\theta -1}}=\sqrt{\frac{{{(\sec \theta -1)}^{2}}}{{{\tan }^{2}}\theta }} $ $ =\frac{\sec \theta -1}{\tan \theta }=cosec\theta -\cot \theta $
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