Trigonometric Equations Question 343
Question: If $ \tan 2\theta \tan \theta =1 $ , then the general value of $ \theta $ is
[Roorkee 1980; Karnataka CET 1992, 93, 2003]
Options:
A) $ ( n+\frac{1}{2} )\frac{\pi }{3} $
B) $ ( n+\frac{1}{2} ),\pi $
C) $ ( 2n\pm \frac{1}{2} )\frac{\pi }{3} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \tan 2\theta =\cot \theta $
Þ $ \tan 2\theta =\tan ( \frac{\pi }{2}-\theta ) $
$ \Rightarrow $ $ 2\theta =n\pi +\frac{\pi }{2}-\theta \Rightarrow \theta =\frac{n\pi }{3}+\frac{\pi }{6} $ .
BETA
