化简:sin方A+sin方(A-π/3)+sin方(A+π/3)

问题描述:

化简:sin方A+sin方(A-π/3)+sin方(A+π/3)

sin方A+sin方(A-π/3)+sin方(A+π/3)
=(1-cos2A)/2+(1-cos(2A-2π/3))/2+(1-cos(2A+2π/3))/2
=3/2-cos2A/2-[cos(2A-2π/3)+cos(2A+2π/3)]/2
=3/2-cos2A/2-cos2Acos4π/3
=3/2-cos2A/2+cos2A/2
=3/2