Trigonometric Equations Question 340
Question: If $ 2\sin \theta +\tan \theta =0 $ , then the general values of $ \theta $ are
Options:
A) $ 2n\pi \pm \frac{\pi }{3} $
B) $ n\pi ,2n\pi \pm \frac{2\pi }{3} $
C) $ n\pi ,2n\pi \pm \frac{\pi }{3} $
D) $ n\pi ,n\pi +\frac{2\pi }{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ 2\sin \theta +\tan \theta =0 $ ; $ \sin \theta ( 2+\frac{1}{\cos \theta } )=0 $ i.e., $ \sin \theta =0\Rightarrow \theta =n\pi $ or $ \frac{1}{\cos \theta }=-2\Rightarrow \cos \theta =-\frac{1}{2}\Rightarrow \theta =2n\pi \pm ( \frac{2\pi }{3} ) $ .
BETA
