SATHEE: Quantitative Aptitude Ques 496

Quantitative Aptitude Ques 496

Question: If $ \sin \theta +\cos \theta =\frac{17}{13}, $ $ 0{}^\circ <\theta <90{}^\circ , $ then the value of $ \sin \theta -\cos \theta $ is

Options:

A) $ \frac{5}{17} $

B) $ \frac{3}{19} $

C) $ \frac{7}{10} $

D) $ \frac{7}{13} $

Show Answer

Answer:

Correct Answer: D

Solution:

$ \sin \theta +\cos \theta =\frac{17}{13} $ On squaring both sides, we get $ {{\sin }^{2}}\theta +{{\cos }^{2}}\theta +2\sin \theta \cos \theta ={{( \frac{17}{13} )}^{2}} $

$ \Rightarrow $ $ 2\sin \theta \cos \theta ={{( \frac{17}{13} )}^{2}}-1 $

$ \Rightarrow $ $ 2\sin \theta \cos \theta =( \frac{17}{13}-1 )( \frac{17}{13}+1 ) $ $ =( \frac{4}{13} )( \frac{30}{13} )=\frac{120}{169} $ Now, $ {{(\sin \theta -\cos \theta )}^{2}}={{(\sin \theta +\cos \theta )}^{2}}-4\sin \theta \cos \theta $ $ ={{( \frac{17}{13} )}^{2}}-2\times \frac{120}{169} $ $ =\frac{289-240}{169}=\frac{49}{169} $

$ \therefore $ $ \sin \theta -\cos \theta =\frac{7}{13} $

Quantitative Aptitude Ques 495

Quantitative Aptitude Ques 497

Quantitative Aptitude Ques 496

Question: If $ \sin \theta +\cos \theta =\frac{17}{13}, $ $ 0{}^\circ <\theta <90{}^\circ , $ then the value of $ \sin \theta -\cos \theta $ is

Options:

Answer:

Solution:

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