Solve `sin^(-1) [sin((2x^(2) + 4)/(1 + x^(2)))] lt pi -3`

Explanation

`sin^(-1)[sin((2x^(2) + 4)/(1 + x^(2)))] lt pi - 3`
Now, `(2x^(2) + 4)/(1 + x^(2)) = (2x^(2) + 2 + 2)/(1 + x^(2)) = 2 + (2)/(1 + x^(2))`
So, `2+(2)/(1 + x^(2)) in (2, 4]`
Therefore, Eq. (i) reduces to
`pi-(2x^(2) + 4)/(1 + x^(2)) lt pi - 3`
or `(2x^(2) + 4)/(1 + x^(2)) gt 3`
or `2x^(2) + 4 gt 3 + 3x^(2)`
or `x^(2) - 1 lt 0`
or `-1 lt x lt1`