The number of solutions of the equation \( \sin ^{-1}\left[x^{2}+\frac{1}{3}\right]+\cos ^{-1}\left[x^{2}-\frac{2}{3}\right]=x^{2} \), for \( x \in[-1,1] \), and \( [\mathrm{x}] \) denotes the greatest integer less than or equal to \( x \), is :

[JEE Main 2021, 17 Mar (Shift 2)]

Question

The number of solutions of the equation \( \sin ^{-1}\left[x^{2}+\frac{1}{3}\right]+\cos ^{-1}\left[x^{2}-\frac{2}{3}\right]=x^{2} \), for \( x \in[-1,1] \), and \( [\mathrm{x}] \) denotes the greatest integer less than or equal to \( x \), is :

[JEE Main 2021, 17 Mar (Shift 2)]

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The number of solutions of the equation \( \sin ^{-1}\left[x^{2}+\frac{1}{3}\right]+\cos ^{-1}\left[x^{2}-\frac{2}{3}\ri…

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