If 6 sin^-1(x^2 -6x +12) = 2 π , then the value of x, is

We hav,

$x^2 - 6x + 12 = (x -3)^2 + 3 ≥ 3 $ for all x

∴ $sin^{-1}(x^2 -6x + 12)$ does not exist.

Thus, there is no value of x satisfying the given equation.