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) \[\theta =\frac{n\pi }{2},n\in Z\]
Correct Answer: B
Solution :
The given equation can be written as \[\Rightarrow \]\[\frac{{{\sin }^{2}}\theta }{\cos \theta }+\sqrt{3}\tan \theta =0\]\[\Rightarrow \] \[\tan \theta \sin \theta +\sqrt{3}\tan \theta =0\] \[\tan \theta (\sin \theta +\sqrt{3})=0\] \[\Rightarrow \] \[\tan \theta =0\] \[\Rightarrow \]\[\theta =n\pi ,\,n\in Z\].
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