The minimum and maximum values of $\cos \left(x+\frac{\pi}{3}\right)+2 \sqrt{2} \sin \left(x+\frac{\pi}{3}\right)$ are respectively

  • A
    $-(2 \sqrt{3}-1)$ and $2 \sqrt{3}-1$
  • B
    $-(1+2 \sqrt{2})$ and $1+2 \sqrt{2}$
  • C
    -$3$ and $3$
  • D
    -$2$ and $2$

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