Trigonometric Equations Question 385
Question: The general solution of $ {{\sin }^{2}}\theta \sec \theta +\sqrt{3}\tan \theta =0 $ is
Options:
A) $ \theta =n\pi +{{(-1)}^{n+1}}\frac{\pi }{3},\theta =n\pi ,n\in Z $
B) $ \theta =n\pi ,n\in Z $
C) $ \theta =n\pi +{{(-1)}^{n+1}}\frac{\pi }{3},n\in Z $
D) $ \theta =\frac{n\pi }{2},n\in Z $
Show Answer
Answer:
Correct Answer: B
Solution:
- The given equation can be written as
$ \Rightarrow $ $ \frac{{{\sin }^{2}}\theta }{\cos \theta }+\sqrt{3}\tan \theta =0 $
$ \Rightarrow $ $ \tan \theta \sin \theta +\sqrt{3}\tan \theta =0 $ $ \tan \theta (\sin \theta +\sqrt{3})=0 $
$ \Rightarrow $ $ \tan \theta =0 $
$ \Rightarrow $ $ \theta =n\pi ,,n\in Z $ .
BETA
