Trigonometric Equations Question 25
Question: If $ \frac{\tan 3\theta -1}{\tan 3\theta +1}=\sqrt{3} $ , then the general value of $ \theta $ is
[MP PET 2004; Orissa JEE 2004]
Options:
A) $ \frac{n\pi }{3}+\frac{\pi }{12} $
B) $ \frac{n\pi }{3}+\frac{7\pi }{36} $
C) $ n\pi +\frac{7\pi }{12} $
D) $ n\pi +\frac{\pi }{12} $
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Answer:
Correct Answer: B
Solution:
- $ \frac{\tan 3\theta -1}{\tan 3\theta +1}=\sqrt{3} $
Þ $ \frac{\tan 3\theta -\tan (\pi /4)}{1+\tan 3\theta ,.,\tan (\pi /4)}=\sqrt{3} $
Þ $ \tan ,( 3\theta -\frac{\pi }{4} )=\tan ,\frac{\pi }{3} $
Þ $ 3\theta -(\pi /4)=n\pi +(\pi /3) $
Þ $ 3\theta =n\pi +\frac{7\pi }{12} $ Þ $ \theta =\frac{n\pi }{3}+\frac{7\pi }{36} $ .
BETA
