Quantitative Aptitude Ques 1473

Question: If $ \sin 5\theta =\cos 20{}^\circ (0{}^\circ <\theta <90{}^\circ ), $ then the value of $ \theta $ is [SSG (CGL) Mains 2014]

Options:

A) $ 4{}^\circ $

B) $ 22{}^\circ $

C) $ 10{}^\circ $

D) $ 14{}^\circ $

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Answer:

Correct Answer: D

Solution:

  • Given, $ \sin 5\theta =\cos 20{}^\circ $

$ \Rightarrow $ $ \sin 5\theta =\sin (90{}^\circ -20{}^\circ ) $

$ \Rightarrow $ $ 5\theta =90{}^\circ -20{}^\circ $

$ \Rightarrow $ $ 5\theta =70{}^\circ $

$ \therefore $ $ \theta =14{}^\circ $