Mathematics - Trigonometric Equation Question with Solution | TestHub

$\begin{array}{rl}& \mathrm{cosec}\theta =\frac{2(\sqrt{3}-1)\pm \sqrt{4(3+1-2\sqrt{3})+16\sqrt{3}}}{2\sqrt{3}}\\ & =\frac{2(\sqrt{3-1})\pm \sqrt{16+8\sqrt{3}}}{2\sqrt{3}}\\ & =\frac{2(\sqrt{3}-1)\pm (2+2\sqrt{3})}{2\sqrt{3}}\end{array}$
$\mathrm{cosec}\theta =2$ or $\frac{-2}{\sqrt{3}}$
$\therefore \sin \theta =\frac{1}{2}$ or $\frac{-\sqrt{3}}{2}$
$\therefore \sin \theta =\frac{1}{2}$ has 3 solutions \& also $\sin \theta =\frac{-\sqrt{3}}{2}$
has 3 solutions in $\left[\frac{-7\pi }{6},\frac{4\pi }{3}\right]$