If the identity cos 4 θ = a cos 4 θ + b cos 2 θ + c holds for some a , b , c ∈ ℚ …

If the identity cos4θ=acos4θ+bcos2θ+c holds for some a,b,c, then a,b,c=
  1. 18,38,12
  2. 18,12,38
  3. 12,18,38
  4. 12,38,18

Solution

Given cos4θ=acos4θ+bcos2θ+c

L.H.S.=cos4θ=12+cos2θ22

=14+12cos2θ+14cos22θ

=14+12cos2θ+1412+cos4θ2

=18cos4θ+12cos2θ+38

Asked in: AP EAMCET 2022 (04 Jul Shift 1)

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