化简sin^2(α-π/6)+sin^2(α+π/6)-sin^2α

题目

化简sin^2(α-π/6)+sin^2(α+π/6)-sin^2α

答案

sin^2(α-π/6)+sin^2(α+π/6)-sin^2α=1/2{1-cos(2α-π/3)+1-cos(2α+π/3)-1+cos2α}=1/2{1+cos2α-2cos2αcosπ/3}=1/2{1+cos2α-cos2α}=1/2