SATHEE: Quantitative Aptitude Ques 916

Quantitative Aptitude Ques 916

Question: If $ \cos \theta +\sin \theta =\sqrt{2}\cos \theta . $ Then, the value of $ \cos \theta -\sin \theta $ is

Options:

A) $ \sqrt{3}\sin \theta $

B) $ \sqrt{2}\cos \theta $

C) $ \sqrt{2}\sin \theta $

D) $ \sqrt{3}\cos \theta $

Show Answer

Answer:

Correct Answer: C

Solution:

Given, $ \cos \theta +\sin \theta =\sqrt{2}\cos \theta $ On squaring both sides, we get $ {{(\cos \theta +\sin \theta )}^{2}}={{(\sqrt{2}\cos \theta )}^{2}} $

$ \Rightarrow $ $ {{\cos }^{2}}\theta +{{\sin }^{2}}\theta +2\sin \theta \cos \theta =2{{\cos }^{2}}\theta $

$ \Rightarrow $ $ 2\sin \theta \cos \theta ={{\cos }^{2}}\theta -{{\sin }^{2}}\theta $

$ \Rightarrow $ $ 2\sin \theta \cos \theta =(\cos \theta -\sin \theta )(\cos \theta +\sin \theta ) $

$ \therefore $ $ \cos \theta -\sin \theta =\frac{2\sin \theta \cos \theta }{(\cos \theta +\sin \theta )} $ $ =\frac{2\sin \theta \cos \theta }{\sqrt{2}\cos \theta }=\sqrt{2}\sin \theta $

Quantitative Aptitude Ques 915

Quantitative Aptitude Ques 917

Quantitative Aptitude Ques 916

Question: If $ \cos \theta +\sin \theta =\sqrt{2}\cos \theta . $ Then, the value of $ \cos \theta -\sin \theta $ is

Options:

Answer:

Solution:

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