If 2 cos θ = 2 - sin θ, then what is the value of cos θ?
Given,
If 2 cosθ = 2 - sinθ
⇒ 2 (cosθ - 1) = -sinθ
Squaring both sides
⇒ 4 (cosθ – 1)2 = sin2θ
⇒ 4 (cosθ – 1)2 = 1 - cos2θ
⇒ 4 cos2θ + 4 - 8 cosθ = 1 - cos2θ
⇒ 5 cos2θ - 8 cosθ + 3 = 0
⇒ 5 cos2θ - 5 cosθ - 3 cosθ + 3 = 0
⇒ 5 cosθ (cosθ – 1) - 3(cosθ – 1) = 0
⇒ (5 cosθ – 3) (cosθ – 1) = 0
⇒ cosθ = 3/5, 1
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