The sides of a triangle are $\sin \alpha ,\,\cos \alpha $ and $\sqrt {1 + \sin \alpha \cos \alpha } $ for some $0 < \alpha < \frac{\pi }{2}$. Then the greatest angle of the triangle is.....$^o$

  • [AIEEE 2004]
  • A

    $150$

  • B

    $90$

  • C

    $120$

  • D

    $60$

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