How on earth is 1-cos(x) equal to 2sin^2(x/2)?

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PreCalculus - Trigonometry: Trig Identities (31 of 57) Proof cos^2(x)=(1+cos2x)/2

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IB HL AA Mathematics Paper 1 (Functions Part 2)

Prove that 1+cosx=2cos^2(x/2) and 1-cosx=2sin^2(x/2) trigonometric identites

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when calculus students use trig identities too early

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