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 $
BETA
