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

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Correct option is D

We have,x2−6x+12=(x−3)2+3≥3 for all x∴ sin−1⁡x2−6x+12 does not exist.Thus, there is no value of x satisfying the given equation.

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If 6 sin−1⁡x2−6x+12=2π, then the value of x, is

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