The number of values of $\mathrm{x}$ in the interval $[0,3 \pi]$ satisfying $2 \sin ^2 x+5 \sin ^2 x-3=0$ is

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Aicharya · Accepted Answer

$\begin{aligned} & 2 \sin ^2 x+5 \sin x-3=0 \ & \Rightarrow(\sin x+3)(2 \sin x-1)=0 \ & \Rightarrow \sin x=-3 	ext { or } \sin x=\frac{1}{2} \ & \Rightarrow 	ext { no solution or } \sin x=\sin \frac{\pi}{6} \ & \Rightarrow x=n \pi+(-1) n \frac{\pi}{6}\end{aligned}$ But $x \in[0,3 \pi]$ $\Rightarrow x=\frac{\pi}{6}, \frac{5 \pi}{6}, \frac{13 \pi}{6}, \frac{17 \pi}{6}$ four solution

The number of values of $\mathrm{x}$ in the interval $[0,3 \pi]$ satisfying $2 \sin ^2 x+5 \sin ^2 x-3=0$ is

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