sin²x/2+2sinx/2-sinx-4cosx/2=0,怎么变成(sinx/2-2cosx/2)(sinx/2+2)=0
问题描述:
sin²x/2+2sinx/2-sinx-4cosx/2=0,怎么变成(sinx/2-2cosx/2)(sinx/2+2)=0
答
sin²x/2+2sinx/2-sinx-4cosx/2=0
sin(x/2)[sin(x/2)+2]-2sin(x/2)cos(x/2)-4cos(x/2)=0
sin(x/2)[sin(x/2)+2]-2cos(x/2)[sin(x/2)+2]=0
提取公因式,即得:
[sin(x/2)-2cos(x/2)]*[sin(x/2)+2]=0