Let $f(\theta)$ is distance of the line $( \sqrt {\sin \theta } )x + (  \sqrt {\cos  \theta })y +1 = 0$ from origin. Then the range of $f(\theta)$ is -

  • A

    $\left[ {\frac{1}{{{2^{\frac{1}{4}}}}},\infty } \right)$

  • B

    $\left[ {1,\sqrt 2 } \right]$

  • C

    $[{1},{\infty } )$

  • D

    $\left[ {\frac{1}{{{2^{\frac{1}{4}}}}},1 } \right]$

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