If $\sin (A + B) =1 $ and $\cos (A - B) = \frac{{\sqrt 3 }}{2},$ then the smallest positive values of $A$ and $ B$ are

  • A

    ${60^o},{\rm{ }}{30^o}$

  • B

    ${75^o},{\rm{ }}{15^o}$

  • C

    ${45^o},{\rm{ }}{60^o}$

  • D

    ${45^o},{\rm{ }}{45^o}$

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