SATHEE: Quantitative Aptitude Ques 2129

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 $

Quantitative Aptitude Ques 2128

Quantitative Aptitude Ques 2130

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