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

Question

If the identity cos 4 θ = a cos 4 θ + b cos 2 θ + c holds for some a , b , c ∈ ℚ , then a , b , c =, 1 8 , 3 8 , 1 2, 1 8 , 1 2 , 3 8, 1 2 , 1 8 , 3 8, 1 2 , 3 8 , 1 8

MARKS App · Accepted Answer

Given cos 4 θ = a cos 4 θ + b cos 2 θ + c L.H.S. = cos 4 θ = 1 2 + cos 2 θ 2 2 = 1 4 + 1 2 cos 2 θ + 1 4 cos 2 2 θ = 1 4 + 1 2 cos 2 θ + 1 4 1 2 + cos 4 θ 2 = 1 8 cos 4 θ + 1 2 cos 2 θ + 3 8

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