化简:(sinx)^2+(sin(x+π/3))^2+(sin(x+2π/3))^2

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化简:(sinx)^2+(sin(x+π/3))^2+(sin(x+2π/3))^2
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化简:(sinx)^2+(sin(x+π/3))^2+(sin(x+2π/3))^2
化简:(sinx)^2+(sin(x+π/3))^2+(sin(x+2π/3))^2

化简:(sinx)^2+(sin(x+π/3))^2+(sin(x+2π/3))^2
利用sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
sin(x+π/3)=1/2sin(x)+(根号3)/2cos(x)
sin(x+2π/3)=-1/2sin(x)+(根号3)/2cos(x)
原式=3/2(sinx)^2+3/2cos(x)^2