SATHEE: Quantitative Aptitude Ques 2016

Quantitative Aptitude Ques 2016

Question: If $ \sin \theta \cos \theta =\frac{\sqrt{3}}{2}, $ then the value of $ {{\sin }^{4}}\theta +{{\cos }^{4}}\theta $ is

Options:

A) $ \frac{7}{8} $

B) $ \frac{5}{8} $

C) $ \frac{3}{8} $

D) $ \frac{1}{8} $

Show Answer

Answer:

Correct Answer: B

Solution:

Given that, $ \sin \theta \cdot \cos \theta =\frac{\sqrt{3}}{4} $ (i) Now, we have $ {{\sin }^{4}}\theta +{{\cos }^{4}}\theta $ $ ={{({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}^{2}}-2{{\sin }^{2}}\theta {{\cos }^{2}}\theta $ $ ={{(1)}^{2}}-2{{(\sin \theta \cos \theta )}^{2}} $ $ =1-2{{( \frac{\sqrt{3}}{4} )}^{2}}=1-2\cdot \frac{3}{16}=1-\frac{3}{8}=\frac{5}{8} $

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Quantitative Aptitude Ques 2016

Question: If $ \sin \theta \cos \theta =\frac{\sqrt{3}}{2}, $ then the value of $ {{\sin }^{4}}\theta +{{\cos }^{4}}\theta $ is

Options:

Answer:

Solution:

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