The number of solutions of $\sin ^2 x+\left(2+2 x-x^2\right) \sin x-3(x-1)^2=0$, where $-\pi \leq x \leq \pi$, is________

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Aicharya · Accepted Answer

$\sin ^2 x-\left(x^2-2 x-2ight) \sin x-3(x-1)^2=0$ $\begin{aligned} & \sin x=-3(	ext { reject }) 	ext { or }(x-1)^2 \ & \sin x=(x-1)^2\end{aligned}$

The number of solutions of $\sin ^2 x+\left(2+2 x-x^2\right) \sin x-3(x-1)^2=0$, where $-\pi \leq x \leq…