Quantitative Aptitude Ques 2129
Question: If $ 2({{\cos }^{2}}\theta -{{\sin }^{2}}\theta )=1, $ where $ \theta $ is a positive acute angle, then the value of $ \theta $ is
Options:
A) $ 60{}^\circ $
B) $ 30{}^\circ $
C) $ 45{}^\circ $
D) $ 22\frac{1}{2}{}^\circ $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ 2({{\cos }^{2}}\theta -{{\sin }^{2}}\theta )=1 $
$ \Rightarrow $ $ {{\cos }^{2}}\theta -{{\sin }^{2}}\theta =\frac{1}{2} $
$ \Rightarrow $ $ 1-{{\sin }^{2}}\theta -{{\sin }^{2}}\theta =\frac{1}{2} $
$ \Rightarrow $ $ 1-2{{\sin }^{2}}\theta =\frac{1}{2} $
$ \Rightarrow $ $ 2{{\sin }^{2}}\theta =1-\frac{1}{2} $
$ \Rightarrow $ $ 2{{\sin }^{2}}\theta =\frac{1}{2} $
$ \Rightarrow $ $ {{\sin }^{2}}\theta =\frac{1}{4} $
$ \Rightarrow $ $ \sin \theta =\frac{1}{2} $
$ \Rightarrow $ $ \theta ={{\sin }^{-1}}( \frac{1}{2} ) $
$ \therefore $ $ \theta =30{}^\circ $
BETA
