The sum of all values of θ∈0,π2 satisfying  sin2⁡2θ+cos4⁡2θ=34, is 

The sum of all values of θ0,π2 satisfying  sin22θ+cos42θ=34, is 

  1. A

    π

  2. B

    π2

  3. C

    3π8

  4. D

    5π4

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    Solution:

    we have , 

    sin22θ+cos42θ=34 

     1cos22θ+cos42θ=34 4cos42θ4cos22θ+1=0 2cos22θ12=0cos4θ=0θ=π8,3π8

    Hence , required sum =π8+3π8=π2

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