sin(x+π/3)=2/3,求sin(x-2π/3)+sin^2(π/6-x)的值
问题描述：
sin(x+π/3)=2/3,求sin(x-2π/3)+sin^2(π/6-x)的值
答
sin(x-2π/3)+sin^2(π/6-x)
=-sin[π+(x-2π/3)]+cos^2[π/2-(π/6-x)]
=-sin(x+π/3)+cos^2(x+π/3)
=-sin(x+π/3)+[1-sin^2(x+π/3)]
=-2/3+(1-4/9)
=-1/9