sin2⁡θ=(x+y)24xy, where x,y∈R, gives real θ if and only if

sin2θ=(x+y)24xy, where x,yR, gives real θ if and only if

  1. A

    x+y=0

  2. B

    x=y

  3. C

    |x|=|y|0

  4. D

    none of these

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    Solution:

     

    We know that

    0sin2θ10(x+y)24xy10(x+y)24xy    [4xy>0](xy)20x=y

    Thus, we have x=y and xy>0

     |x|=|y|0

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