Find all the principle value for cos inverse of -1/2?

We know that range of the principal value branch of cos-1 is 0, π.Let cos-1-12 = θcos θ = -12cos θ = - cos π3cos θ = cosπ - π3 = cos2π3θ = 2π3 0, π

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cos-1( -1/2)  = π – cos-1(1/2)  [ cos-1(-x) = π – cos-1(x) ]
                = π – π/3 =2 π/3 .Hope that helps.
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