Trigonometric Equations Question 361
Question: If $ \cos 2\theta +3\cos \theta =0 $ , then the general value of $ \theta $ is
Options:
A) $ 2n\pi \pm {{\cos }^{-1}}\frac{-3+\sqrt{17}}{4} $
B) $ 2n\pi \pm {{\cos }^{-1}}\frac{-3-\sqrt{17}}{4} $
C) $ n\pi \pm {{\cos }^{-1}}\frac{-3+\sqrt{17}}{4} $
D) $ n\pi \pm {{\cos }^{-1}}\frac{-3-\sqrt{17}}{4} $
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Answer:
Correct Answer: A
Solution:
- $ 2{{\cos }^{2}}\theta -1+3\cos \theta =0 $ $ \cos \theta =\frac{-3\pm \sqrt{9+8}}{4}=\frac{-3\pm \sqrt{17}}{4} $
$ \Rightarrow $ $ \theta =2n\pi \pm {{\cos }^{-1}}( \frac{-3+\sqrt{17}}{4} ) $ , (Taking +ve sign).
BETA
