A maths 一問

1.cosx+cos3X=0
2cos(2x)cosx=0
2cos(2x)=0 or cosx=0
2x=90+-180n or x=90+-180n
x=45+-90n or x=90+-180n


2.cosx-cos3x=sinx-si n3x
2sin(2x)sinx=-2cos(2x)sinx
sin(2x)sinx=-cos(2x)sinx
sinx=0 or tan(2x)=-1
x=+-180n or 2x=-45+-180n
x=+-180n or x=-22.5+-90n


3.sin3x+cos3x=sin2x+ cos2x
sin3x-sin2x=cos2x-cos3x
2cos(2.5x)sin(0.5x)=-2sin(2.5x)sin(-0.5x)
cos(2.5x)sin(0.5x)=sin(2.5x)sin(0.5x)
sin(0.5x)=0 or tan(2.5x)=1
x=+-180n or 2.5x=45+-180n
x=+-180n or x=18+-72n

2007-04-21 22:42:32 補充：
-----------cosx+cos2x+cos3X+cos4x=0 2cos(2x)cos(x)+2cos(3x)cos(x)=0cosx(cos2x+cos3x)=0cosx=0 or cos2x+cos3x=0x=90+-180n or 2cos(2.5x)cos(0.5x)=0x=90+-180n or cos(2.5x)=0 or cos(0.5x)=0x=90+-180n or 2.5x=90+-180n or 0.5x=90+-180n x=90+-180n or x=36+-72n or x=180+-360n

2.cosx-cos3x=sinx-sin3x