sin（6/π-α）=1/3,则cos（2π/3+2α）的值为

题目

sin（6/π-α）=1/3,则cos（2π/3+2α）的值为

答案

cos(2π/3+2α)= - cos（π-(2π/3+2α)）=- cos(π/3-2α)=- cos(2α-π/3) (公式cos2α=1-2(sinα)^2）=- (1-2(sin(α-π/6))^2)∵sin(π/6-α)=1/3 ∴sin(α-π/6))^2=1/9故cos(2π/3+2α)= -(1-2*1/9) =-7/9...