Question

已知cos(π/6-a)=根号3/3,求cos(5π/6+a)-sin²(a-π/6)的值.？

Answer 1

cos(π/6-a)=√3/3,
∴ cos(5π/6+a)=cos〔π-(5π/6-a)〕=- cos(π/6-a)=-√3/3
sin²(a-π/6)=1- cos ²(a-π/6) =1- cos(π/6-a)=1-（-√3/3）2 =1-1/3=2/3
cos(5π/6+a)-sin²(a-π/6)= -√3/3-2/3,4,∵cos(π/6-a)=√3/3
∴cos(5π/6+a)-sin²(a-π/6)=cos(π-(π/6-a))-1+cos²(a-π/6)
=-cos(π/6-a)-1+cos²(π/6-a)
=-(√3/3)-1+(√3/3)²
=-√3/3-1+1/3
=-(2+√3)/3。,0,已知cos(π/6-a)=根号3/3,求cos(5π/6+a)-sin²(a-π/6)的值.