Trigonometric Identities Question 258
Question: Which one of the following is one of the solutions of the equation of the equation $ \tan 2\theta .\tan \theta =1 $ ?
Options:
A) $ \pi /12 $
B) $ \pi /6 $
C) $ \pi /4 $
D) $ \pi /3 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \tan 2\theta .tan\theta =1 $
$ \Rightarrow ,\frac{2\tan \theta }{1-{{\tan }^{2}}\theta }.\tan \theta =1 $
$ \Rightarrow 2{{\tan }^{2}}\theta =1-{{\tan }^{2}}\theta \Rightarrow 3{{\tan }^{2}}\theta =1 $
$ \Rightarrow ,{{\tan }^{2}}\theta =\frac{1}{3}={{( \frac{1}{\sqrt{3}} )}^{2}} $
$ \Rightarrow ,{{\tan }^{2}}\theta ={{\tan }^{2}}(30{}^\circ )={{\tan }^{2}}( \frac{\pi }{6} ) $ $ [ \because ,\theta =n\pi \pm \frac{\pi }{6} ]; $
$ \therefore \theta =\frac{\pi }{6} $
BETA
