Question

The most general value of $\theta$ which satisfies both the equations $\tan \theta=\sqrt{3}$ and $\operatorname{cosec} \theta=-\frac{2}{\sqrt{3}}$ is-

• A. $n \pi+\frac{4 \pi}{3} ; n \in I$
• B. $n \pi+\frac{2 \pi}{3} ; n \in I$
• C. $2 n \pi+\frac{4 \pi}{3} ; n \in I$
• D. $2 n \pi+\frac{2 \pi}{3} ; n \in I$

Answer 1

Answer: (C)

$\tan \theta=\sqrt{3}$ and $\sin \theta=-\frac{\sqrt{3}}{2}$ are both satisfied for only one value of $\theta=\frac{4 \pi}{3}, \theta \in[0,2 \pi]$
$\therefore$ aeneral solution is $2 n \pi+4 \pi$