Let (sin⁡a)x2+(sin⁡a)x+1−cos⁡a=0 The set of values of a for which roots of this equation are real and distinct, is

Let (sina)x2+(sina)x+1cosa=0 The set of values of a for which roots of this equation are real and distinct, is

  1. A

    (0, 2tan114)

  2. B

    0,2π3

  3. C

    (0, π)

  4. D

    (0, 2π)

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    Solution:

    The roots of the given equation will be real and distinct, iff

     sin2a4sina(1cosa)>0(1cosa){1+cosa4sina}>02cos2a28sina2cosa2>02cos2a2(14tana2)>04tana2<1π2<a2<tan114π<a<2tan114

    Hence, option (a) is correct.

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