Quantitative Aptitude Ques 2014

Question: What is the value of $ \frac{\sin \theta }{1+\cos \theta }+\frac{1+\cos \theta }{\sin \theta }? $

Options:

A) $ 2coses\theta $

B) $ 2\sec \theta $

C) $ \sec \theta $

D) $ cosec\theta $

Show Answer

Answer:

Correct Answer: A

Solution:

  • Let $ f,(\theta )=\frac{\sin \theta }{1+\cos \theta }+\frac{1+\cos \theta }{\sin \theta } $ $ =\frac{{{\sin }^{2}}\theta +{{(1+\cos \theta )}^{2}}}{\sin \theta (1+\cos \theta )} $ $ =\frac{{{\sin }^{2}}\theta +1+{{\cos }^{2}}\theta +2\cos \theta }{\sin \theta (1+\cos \theta )} $ $ =\frac{2+2\cos \theta }{\sin \theta (1+\cos \theta )} $ $ =\frac{2(1+\cos \theta )}{\sin \theta (1+\cos \theta )} $ $ =2cosec\theta $
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