Mathematics - Trigonometric Equation Question with Solution | TestHub

$\begin{array}{rl}& (4-\sqrt{3})\sin x-2\sqrt{3}{\cos }^{2}x=\frac{-4}{1+\sqrt{3}},x\in \left[-2\pi ,\frac{5\pi }{2}\right]\\ & \Rightarrow (4-\sqrt{3})\sin x-2\sqrt{3}\left(1-{\sin }^{2}x\right)=2(1-\sqrt{3})\\ & \Rightarrow 2\sqrt{3}{\sin }^{2}x+4\sin x-\sqrt{3}\sin x-2=0\\ & \Rightarrow (2\sin x-1)(\sqrt{3}\sin x+2)=0\\ & \Rightarrow \sin x=\frac{1}{2}\\ & \therefore \text{ Number of solution }=5\end{array}$