If $\tan \theta + \sin \theta = a$ and $\tan \theta - \sin \theta = b$,then the values of $\cot \theta$ and $\operatorname{cosec} \theta$ are respectively

  • A
    $\frac{1}{a+b}, \frac{1}{a-b}$
  • B
    $\frac{2}{a+b}, \frac{2}{a-b}$
  • C
    $\frac{2}{a-b}, \frac{2}{a+b}$
  • D
    $\frac{1}{a-b}, \frac{1}{a+b}$

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