cosπ/12*cosπ/12 - cosπ/6*sinπ/6 =cos²π/12- (1/2)*sin2*π/6 =
=(1/2)*(1+cos2*π/12 )- (1/2)*sin(π/3) =(1/2)*(1+cos(π/6) -sin(π/3)) =
(1/2)*(1+√3/2 -3/2) =1/2.

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Использованы формулы :
sinα*cosα =(sin2α)/2 и cos²α =(1+cos2α)/2 .