SATHEE: Quantitative Aptitude Ques 977

Quantitative Aptitude Ques 977

Question: The value of $ \frac{1}{cosec\theta -cot\theta }-\frac{1}{\sin \theta }, $ is

Options:

A) $ \cot \theta $

B) $ cosec\theta $

C) $ \tan \theta $

D) $ 1 $

Show Answer

Answer:

Correct Answer: A

Solution:

$ \frac{1}{cosec\theta -cot\theta }-\frac{1}{\sin \theta } $ $ =\frac{1}{\frac{1}{\sin \theta }-\frac{\cos \theta }{\sin \theta }}-\frac{1}{\sin \theta }=\frac{\sin \theta }{1-\cos \theta }-\frac{1}{\sin \theta } $ $ =\frac{{{\sin }^{2}}\theta -(1-\cos \theta )}{(1-\cos \theta )\sin \theta } $ $ =\frac{1-{{\cos }^{2}}\theta -1+\cos \theta }{(1-\cos \theta )\sin \theta } $ $ [\because {{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1] $ $ =\frac{\cos \theta (1-\cos \theta )}{(1-\cos \theta )\sin \theta }=\frac{\cos \theta }{\sin \theta }=\cot \theta $

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