Trigonometric Equations Question 295
If $ \cos \theta +\cos 7\theta +\cos 3\theta +\cos 5\theta =0 $ , then $ \theta = \frac{\pi}{4} + \frac{k\pi}{4} $ for any integer $ k $
[Dhanbad Engg. 1972]
Options:
A) $ \frac{n\pi }{4} $
B) $ \frac{n\pi }{2} $
C) $ \frac{n\pi }{8} $
D) None of these
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Answer:
Correct Answer: C
Solution:
- Combining $ \theta $ and $ 7\theta $ , $ 3\theta $ and $ 5\theta $ , we get $ 2\cos 4\theta (\cos 3\theta +\cos \theta )=0 $
Þ $ 4\cos 4\theta ,\cos 2\theta \cos \theta =0 $
Þ $ 4\frac{1}{2^{3}\sin \theta } $ $ (\sin 2^{3}\theta )=0 $ ; $ \sin 8\theta =0 $ . Hence $ \theta =\frac{n\pi }{8} $ .
BETA
