SATHEE: Quantitative Aptitude Ques 2166

Quantitative Aptitude Ques 2166

Question: If $ \frac{{{\cos }^{2}}\theta }{{{\cot }^{2}}\theta -{{\cos }^{2}}\theta }=3 $ and $ 0{}^\circ <\theta <90{}^\circ , $ then the value of $ \theta $ is

Options:

A) $ 30{}^\circ $

B) $ 45{}^\circ $

C) $ 60{}^\circ $

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

$ \frac{{{\cos }^{2}}\theta }{{{\cot }^{2}}\theta -{{\cos }^{2}}\theta }=3 $

$ \Rightarrow $ $ {{\cos }^{2}}\theta =3{{\cot }^{2}}\theta -3{{\cos }^{2}}\theta $

$ \Rightarrow $ $ 4{{\cos }^{2}}\theta =3{{\cot }^{2}}\theta $

$ \Rightarrow $ $ 4{{\cos }^{2}}\theta -\frac{3{{\cos }^{2}}\theta }{{{\sin }^{2}}\theta }=0 $

$ \Rightarrow $ $ {{\cos }^{2}}\theta ( 4-\frac{3}{{{\sin }^{2}}\theta } )=0 $

$ \Rightarrow $ $ 4-\frac{3}{{{\sin }^{2}}\theta }=0 $

$ \Rightarrow $ $ 4{{\sin }^{2}}\theta -3=0 $

$ \Rightarrow $ $ {{\sin }^{2}}\theta =\frac{3}{4} $

$ \Rightarrow $ $ \sin \theta =\frac{\sqrt{3}}{2}=\sin 60{}^\circ $

$ \therefore $ $ \theta =60{}^\circ $

Quantitative Aptitude Ques 2165

Quantitative Aptitude Ques 2167

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