Trigonometric Equations Question 9
Question: If $ \cos \theta +\cos 2\theta +\cos 3\theta =0 $ , then the general value of $ \theta $ is
[UPSEAT 2003]
Options:
A) $ \theta =2m\pi \pm \frac{2\pi }{3} $
B) $ \theta =2m\pi \pm \frac{\pi }{4} $
C) $ \theta =m\pi \pm {{(-1)}^{m}}\frac{2\pi }{3} $
D) $ x=m\pi +{{(-1)}^{m}}\frac{\pi }{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \cos \theta +\cos 2\theta +\cos 3\theta =0 $
Þ $ (\cos \theta +\cos 3\theta )+\cos 2\theta =0 $
Þ $ 2\cos 2\theta \cos \theta +\cos 2\theta =0 $
Þ $ \cos 2\theta (2\cos \theta +1)=0 $
Þ $ \cos 2\theta =0=\cos \frac{\pi }{2} $
Þ $ \theta =\frac{\pi }{4} $ Þ $ \theta =2m\pi \pm \frac{\pi }{4} $ or $ \cos \theta =\frac{-1}{2}=\cos \frac{2\pi }{3} $
Þ $ \theta =2m\pi \pm \frac{2\pi }{3} $ .
BETA
