已知cosa(π/6-α)=根号3/3 ,求sin(π/2+α)

已知 cosa(π/6-α)=√3 / 3求sin(π/2+α) 方法1：cos(α - β) = cosαcosβ + sinα sinβcosa(π/6-α) = cosπ/6*cosα + sinπ/6* sinα =√3 / 2*cosα + 1/2* sinα = √3 / 3所以：√3 / 2*cosα + 1/2* √(1 - cos²α) = √3 / 31 - cos²α = 4 (√3 / 3 - √3 / 2*cosα) ²12cos²α - 12cosα +1 = 0解得：cosα = [3 ±√6] / 6 答案：sin(π/2+α) = cosα ＝ [3 ±√6] / 6