Question

The general solution of $\sin ^{2} \,\theta\, \sec \,\theta+\sqrt{3} \tan \,\theta=0$ is

• 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. $\theta=\frac{ n \pi}{2}, n \in Z$

Answer 1

Answer: (B)

The given equation can be written as
$\frac{\sin ^{2} \,\theta}{\cos\,\theta}+\sqrt{3} \tan \,\theta=0 \Rightarrow \tan \,\theta \sin\, \theta+\sqrt{3} \tan\, \theta=0$
$\tan \,\theta(\sin \,\theta+\sqrt{3})=0$ as $\sin \,\theta \neq-\sqrt{3}$
Hence, $\tan \,\theta=0$
$ \Rightarrow \theta= n \pi, n \in Z$