Trigonometric Equations Question 370
Question: The general value of satisfying the equation $ \tan \theta +\tan ( \frac{\pi }{2}-\theta )=2 $ , is
[MNR 1974]
Options:
A) $ n\pi +\frac{\pi }{4} $
B) $ n\pi +\frac{\pi }{4} $
C) $ 2n\pi \pm \frac{\pi }{4} $
D) $ n\pi +{{(-1)}^{n}}\frac{\pi }{4} $
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Answer:
Correct Answer: B
Solution:
- $ \tan \theta +\frac{1}{\tan \theta }=2 $
$ \Rightarrow $ $ {{\tan }^{2}}\theta -2\tan \theta +1=0 $
$ \Rightarrow $ $ \tan \theta =1=\tan \frac{\pi }{4} $
$ \Rightarrow $ $ \theta =n\pi +\frac{\pi }{4} $ .
BETA
