方程sin(x+π/3)=sin(π/3)-sinx的解集

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方程sin(x+π/3)=sin(π/3)-sinx的解集
方程sin(x+π/3)=sin(π/3)-sinx的解集

方程sin(x+π/3)=sin(π/3)-sinx的解集
sin(x+π/3)=sin(π/3)-sinx
sinxcos(π/3)+cosxsin(π/3)=sin(π/3)-sinx
1/2sinx+√3/2cosx=√3/2-sinx
3/2sinx+√3/2cosx=√3/2
√3/2sinx+1/2cosx=1/2
sinxcos(π/6)+cosxsin(π/6)=1/2
sin(x+π/6)=1/2
x+π/6=π/6+2kπ或x+π/6=5π/6+2kπ
x=2kπ或x=2π/3+2kπ(k为整数)

£是怕值
sinxcos£/3+cosxsin£/3=sin£/3-sinx,
(3/2)sinx+(根3/2)cosx=根3/2,提取根3得,sin(x+£/6)=1/2求解即可