Trigonometric Equations Question 347
Question: If $ \frac{1-\cos 2\theta }{1+\cos 2\theta }=3 $ , then the general value of $ \theta $ is
Options:
A) $ 2n\pi \pm \frac{\pi }{6} $
B) $ n\pi \pm \frac{\pi }{6} $
C) $ 2n\pi \pm \frac{\pi }{3} $
D) $ n\pi \pm \frac{\pi }{3} $
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Answer:
Correct Answer: D
Solution:
- $ \frac{1-\cos 2\theta }{1+\cos 2\theta }=3 $
Þ $ \frac{1-(1-2{{\sin }^{2}}\theta )}{1+(2{{\cos }^{2}}\theta -1)}=3 $
$ \Rightarrow $ $ {{\tan }^{2}}\theta =3 $
$ \Rightarrow $ $ \theta =n\pi \pm \frac{\pi }{3} $ .
BETA
