Solve this cos 2theta - cos theta = 0
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Given : Cos 2θ - Cosθ = 0
To Find : Value of θ
Solution:
Cos 2θ - Cosθ = 0
Cos 2θ = 2Cos²θ - 1
=> 2Cos²θ - 1 - Cosθ = 0
=> 2Cos²θ - Cosθ - 1 = 0
=> 2Cos²θ - 2Cosθ + Cosθ - 1 = 0
=> 2Cosθ(Cosθ - 1) + 1 (Cosθ - 1 ) = 0
=> (Cosθ - 1) ( 2Cosθ + 1) = 0
=> Cosθ - 1 = 0 or 2Cosθ + 1 = 0
=> Cosθ = 1 or Cosθ = - 1/2
θ = 0° , 120°
=> θ = ±2nπ or θ = 2π/3 ± 2nπ
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