Question 17.2.4: Find the general value of x for which √3 cosec x=2 ....

Given: \sqrt{3} \operatorname{cosec} x=2 \Rightarrow \operatorname{cosec} x=\frac{2}{\sqrt{3}} \Rightarrow \sin x=\frac{\sqrt{3}}{2} .

The least value of x in \left[0,2 \pi\left[\right.\right. for which \sin x=\frac{\sqrt{3}}{2} is \frac{\pi}{3} .

\therefore \quad \sin x=\sin \frac{\pi}{3} \Rightarrow x=\left\{n \pi+(-1)^{n} \cdot \frac{\pi}{3}\right\} , where n \in I .

Hence, the general solution is x=\left\{n \pi+(-1)^{n} \cdot \frac{\pi}{3}\right\} , where n \in I .