Suppose that the sides $a,b, c$ of a triangle $A B C$ satisfy $b^2=a c$. Then the set of all possible values of $\frac{\sin A \cot C+\cos A}{\sin B \cot C+\cos B}$ is

  • [KVPY 2021]
  • A

    $(0, \infty)$

  • B

    $\left(0, \frac{\sqrt{5}+1}{2}\right)$

  • C

    $\left(\frac{\sqrt{5}-1}{2}, \frac{\sqrt{5}+1}{2}\right)$

  • D

    $\left(\frac{\sqrt{5}-1}{2}, \infty\right)$

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