Trigonometric Equations Question 349
Question: If $ \cos 7\theta =\cos \theta -\sin 4\theta $ , then the general value of $ \theta $ is
Options:
A) $ \frac{n\pi }{4},\frac{n\pi }{3}+\frac{\pi }{18} $
B) $ \frac{n\pi }{3},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18} $
C) $ \frac{n\pi }{4},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18} $
D) $ \frac{n\pi }{6},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18} $
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Answer:
Correct Answer: C
Solution:
- $ \sin 4\theta =\cos \theta -\cos 7\theta $
Þ $ \sin 4\theta =2\sin (4\theta )\sin (3\theta ) $
$ \Rightarrow $ $ \sin 4\theta =0\Rightarrow $ $ 4\theta =n\pi $ or $ \sin 3\theta =\frac{1}{2}=\sin ( \frac{\pi }{6} ) $
$ \Rightarrow $ $ 3\theta =n\pi +{{(-1)}^{n}}\frac{\pi }{6}\Rightarrow \theta =\frac{n\pi }{4},,\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18} $ .
BETA
