If cos (PAI / 6-A) = root 3 / 3, then the square of sin (a-pai / 6) - cos (5pai / 6 + a) is
Sin (a-pai / 6) square = 1-cos (a-pai / 6) square = 1-cos (PAI / 6-A) square = 1 - (root 3 / 3) square = 2 / 3
Cos (5pai / 6 + a) = cos (- 5pai / 6-A) = - cos (pai-5pai / 6-A) = cos (PAI / 6-A) = radical 3 / 3
Original formula = 2 / 3-radical 3 / 3
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