- sin(x+π/3)+2sin(x
- sin(x+π/3)+2sin(x-π/3)-√3c(2π/3-x)=
- 注意到2pi/3-x=pi-(pi/3+x)--->cos(2pi/3-x)=-cos(x+pi/3)
sin(x+π/3)+2sin(x-π/3)-√3cos(2π/3-x)
=sin(x+pi/3)+√3cos(x+pi/3)+2sin(x-pi/3)
=2sin[(x+pi/3)+pi/3)]-2sin(x+pi/3)
=2[sin(x+2pi/3+sin(x+pi/3)]
=2*2sin(x+pi/2)cos(pi/6) (和差化积得来)
=2√3cosx.
实际上可以直接用二角和公式也可以得出同样结果。