已知cos(π/6-α)=根号3/3,求cos(5π/6+α)-sin²(-α+7π/6)的值.求详解,

题目

已知cos(π/6-α)=根号3/3,求cos(5π/6+α)-sin²(-α+7π/6)的值.求详解,

答案

cos(π/6-α)=根号3/3
cos(5π/6+α)-sin²(-α+7π/6)
=cos[π-(π/6-a)]-sin²[π+(π/6-a)]
=-cos(π/6-a)-sin²(π/6-a)
=-√3/3-[1-cos²(π/6-a)]
=-√3/3-(1-1/3)
=-√3/3-2/3