Trigonometric Equations Question 55
Question: The values of $ \theta $ satisfying $ \sin 7\theta =\sin 4\theta -\sin \theta $ and $ 0<\theta <\frac{\pi }{2} $ are
[EAMCET 1990]
Options:
A) $ \frac{\pi }{9},\frac{\pi }{4} $
B) $ \frac{\pi }{3},\frac{\pi }{9} $
C) $ \frac{\pi }{6},\frac{\pi }{9} $
D) $ \frac{\pi }{3},\frac{\pi }{4} $
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Answer:
Correct Answer: A
Solution:
- $ \sin 7\theta +\sin \theta -\sin 4\theta =0 $
$ \Rightarrow $ $ 2\sin 4\theta \cos 3\theta -\sin 4\theta =0 $
$ \Rightarrow $ $ \sin 4\theta (2\cos 3\theta -1)=0\Rightarrow \sin 4\theta =0,,\cos 3\theta =\frac{1}{2} $ Now sin $ 4\theta =0 $
$ \Rightarrow $ $ 4\theta =\pi $
$ \Rightarrow $ $ \theta =\frac{\pi }{4} $ . and $ \cos 3\theta =\frac{1}{2} $
$ \Rightarrow $ $ 3\theta =\frac{\pi }{3} $
$ \Rightarrow $ $ \theta =\frac{\pi }{9} $ .
BETA
