Question:
can anyone please help me on this equation prove cos 4θ = 8 cos (5) 4 θ − 8cos2 θ 1. in complex numbers
Answer:
Given cos 4θ = cos (2*2θ)
=> cos 4θ = 1 - 2sin2 (2θ)
=> cos 4θ = 1 - 2{sin(2θ)}2
=> cos 4θ = 1 - 2{2*sinθ*cosθ}2
=> cos 4θ = 1 - 2*4*sin2 θ*cos2 θ
=> cos 4θ = 1 - 8*sin2 θ*cos2 θ
=> cos 4θ = 1 - 8*(1 - cos2 θ)*cos2 θ
=> cos 4θ = 1 - 8cos2 θ + 8cos4 θ
=> cos 4θ = 8cos4 θ - 8cos2 θ + 1
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