Quantitative Aptitude Ques 2286

Question: What is $ \sqrt{\frac{1+\sin \theta }{1-\sin \theta }} $ equal to?

Options:

A) $ \sec \theta -\tan \theta $

B) $ \sec \theta +\tan \theta $

C) $ \cos ec\theta +\cot \theta $

D) $ \cos ec\theta -\cot \theta $

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ \sqrt{\frac{1+\sin \theta }{1-\sin \theta }} $ On multiplying with $ 1+\sin \theta $ in numerator and denominator, we get $ \sqrt{\frac{(1+\sin \theta )}{(1-\sin \theta )}\times \frac{(1+\sin \theta )}{(1+\sin \theta )}} $ $ =\sqrt{\frac{{{(1+\sin \theta )}^{2}}}{1-{{\sin }^{2}}\theta }}=\sqrt{\frac{{{(1+\sin \theta )}^{2}}}{{{\cos }^{2}}\theta }} $

$ \Rightarrow $ $ \frac{1+\sin \theta }{\cos \theta }=\frac{1}{\cos \theta }+\frac{\sin \theta }{\cos \theta } $ $ =\sec \theta +\tan \theta $

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