The number of solutions of equation $(4-\sqrt{3}) \sin x$ $-2 \sqrt{3} \cos ^2 x=-\frac{4}{1+\sqrt{3}}, x \in\left[-2 \pi, \frac{5 \pi}{2}\right]$ is

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Aicharya · Accepted Answer

$\begin{aligned} & (4-\sqrt{3}) \sin x-2 \sqrt{3} \cos ^2 x=\frac{-4}{1+\sqrt{3}}, x \in\left[-2 \pi, \frac{5 \pi}{2}ight] \ & \Rightarrow(4-\sqrt{3}) \sin x-2 \sqrt{3}\left(1-\sin ^2 xight)=2(1-\sqrt{3}) \ & \Rightarrow 2 \sqrt{3} \sin ^2 x+4 \sin x-\sqrt{3} \sin x-2=0 \ & \Rightarrow(2 \sin x-1)(\sqrt{3} \sin x+2)=0 \ & \Rightarrow \sin x=\frac{1}{2} \ & 	herefore 	ext { Number of solution }=5\end{aligned}$ ,

The number of solutions of equation $(4-\sqrt{3}) \sin x$ $-2 \sqrt{3} \cos ^2 x=-\frac{4}{1+\sqrt{3}}, x…

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