Question

Find the sum of values of x(in degrees) if $\text{cosec}x=\frac{2\sqrt{3}}{3}forx\in [0,{\pi }^c]$

Answer 1

$cosecx=\left(\frac{2\sqrt{3}}{3}\right)=\left(\frac{2}{\sqrt{3}}\right)sinx=\left(\frac{\sqrt{3}}{2}\right)\therefore x=\left(\frac{\pi }{6}\right)and\left(\frac{5\pi }{6}\right)\therefore \left(\frac{\pi }{6}\right)+\left(\frac{5\pi }{6}\right)=\pi ={180}^{\circ }$