Quantitative Aptitude Ques 1583

Question: If $ \frac{\cos x}{cosecx+1}+\frac{\cos x}{cosecx-1}=2, $ which one of the following is one of the value of x?

Options:

A) $ \frac{\pi }{2} $

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

C) $ \frac{\pi }{4} $

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

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ \frac{\cos x}{cosecx+1}+\frac{\cos x}{cosecx-1}=2 $

$ \Rightarrow $ $ \frac{\cos x(cosecx-1)+\cos x(cosecx+1)}{(cosecx+1)(cosecx-1)} $

$ \Rightarrow $ $ \frac{\cos xcosecx-\cos x+\text{cos }xcosecx+\cos x}{cose{c^{2}}x-1}=2 $

$ \Rightarrow $ $ \frac{2\cos xcosecx}{{{\cot }^{2}}x}=2 $
$ \Rightarrow $ $ \frac{2\cot x}{{{\cot }^{2}}x}=2 $

$ \Rightarrow $ $ \cot x=1 $
$ \Rightarrow $ $ x=\frac{\pi }{4} $

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