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steps to derive Cosine (StartFraction x Over 2 EndFraction) = plus-or-minus StartRoot StartFraction 1 + cosine (x) Over 2 EndFraction EndRoot are:

Cosine squared theta = StartFraction 1 + cosine (2 theta) Over 2 EndFraction.Let theta = StartFraction x Over 2 EndFraction: cosine squared (x) = StartStartFraction 1 + cosine (2 (StartFraction x Over 2 EndFraction) ) OverOver 2 EndFraction EndEndFraction
Cosine squared (StartFraction x Over 2 EndFraction) = StartFraction 1 + cosine (x) Over 2 EndFraction
Cosine (StartFraction x Over 2 EndFraction) = plus-or-minus StartRoot StartFraction 1 + cosine (x) Over 2 EndFraction EndRoot
Provide the justifications for steps in the derivation shown.
identity

Simplifying

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