If the equation sin4θ+cos4θ=a has a real solution then

If the equation sin4θ+cos4θ=a has a real solution then

  1. A

    a12

  2. B

    a12

  3. C

    12a1

  4. D

    a0

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    Solution:

    We have,

       a=sin4θ+cos4θsin2θ+cos2θ1

    Also, 

                 a=sin4θ+cos4θ=sin2θ+cos2θ22sin2θcos2θ a=sin4θ+cos40=112sin22θ sin220=2(1a)2(1a)1a12

    Hence, 12a1

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