If $\tan \theta = \frac{a}{b},$ then $\frac{{\sin \theta }}{{{{\cos }^8}\theta }} + \frac{{\cos \theta }}{{{{\sin }^8}\theta }} = $

  • A

    $ \pm \frac{{{{({a^2} + {b^2})}^4}}}{{\sqrt {{a^2} + {b^2}} }}\left( {\frac{a}{{{b^8}}} + \frac{b}{{{a^8}}}} \right)$

  • B

    $ \pm \frac{{{{({a^2} + {b^2})}^4}}}{{\sqrt {{a^2} + {b^2}} }}\left( {\frac{a}{{{b^8}}} - \frac{b}{{{a^8}}}} \right)$

  • C

    $ \pm \frac{{{{({a^2} - {b^2})}^4}}}{{\sqrt {{a^2} + {b^2}} }}\left( {\frac{a}{{{b^8}}} + \frac{b}{{{a^8}}}} \right)$

  • D

    $ \pm \frac{{{{({a^2} - {b^2})}^4}}}{{\sqrt {{a^2} - {b^2}} }}\left( {\frac{a}{{{b^8}}} - \frac{b}{{{a^8}}}} \right)$

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