evaluate cos{pi/3 - cos-1 (1/2)}

We know that range of the principal value branch of cos-1 is 0,π.Let cos-112 = θcos θ = 12cos θ = cos π3θ = π30,πSo, principal value of cos-112 = π3Now, cosπ3 - cos-112 = cosπ3-π3 = cos 0 =  1

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cos(pi/3 - pi/3) as cos^-1(1/2)=pi/3
therefore, cos(0)=1
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