SATHEE: Quantitative Aptitude Ques 1589

Quantitative Aptitude Ques 1589

Question: If $ 5\sin \theta +12\cos \theta =13, $ then what is $ 5\cos \theta -12\sin \theta $ equal to?

Options:

A) $ -2 $

B) $ -1 $

C) $ 0 $

D) $ 1 $

Show Answer

Answer:

Correct Answer: C

Solution:

$ \because $ $ 5\sin \theta +12\cos \theta =13 $ On squaring both sides, we get $ 25{{\sin }^{2}}\theta +144{{\cos }^{2}}\theta +120\sin \theta \cos \theta =169 $

$ \Rightarrow $ $ 25(1-{{\cos }^{2}}\theta )+144(1-{{\sin }^{2}}\theta ) $ $ +120\sin \theta \cos \theta =169 $

$ \Rightarrow $ $ 25-25{{\cos }^{2}}\theta +144-144{{\sin }^{2}}\theta $ $ +120\sin \theta \cos \theta =169 $

$ \Rightarrow $ $ 25{{\cos }^{2}}\theta +144{{\sin }^{2}}\theta -120\sin \theta \cos \theta =169-169 $

$ \Rightarrow $ $ {{(5\cos \theta -12\sin \theta )}^{2}}=0 $

$ \Rightarrow $ $ 5\cos \theta -12\sin \theta =0 $

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