求cosx-cos3x=2sin2xsinx的详细化简过程

求cosx-cos3x=2sin2xsinx的详细化简过程，再线等待高手解决~！！

2024-12-29 23:09:55

推荐回答（3个）

回答1：

cosx-cos^3 x=2sin^2 xsinx
cosx(1-cos^2 x)=2sin^2 xsinx
cosxsin^2 x=2sin^2 xsinx
cosx=2sinx 或者sinx=0
x=arctan1/2或者x=0

回答2：

cosx-cos3x=cosx-[cos2xcosx-sin2xsinx]
=cosx-cos2xcosx+sin2xsinx
=cosx(1-cos2x)+sin2xsinx
=cosx*2sin^2x+sin2xsinx
=sin2xsinx+sin2xsinx
=2sin2xsinx

回答3：

cosx-cos3x=cosx-cos(x+2x)=cosx-cosxcos2x+sinxsin2x=cosx-cosx(1-2sin^2x)+2sin^2xcosx=cosx-cosx+4sin^2xcosx
=4sin^2xcosx
=2sinx(2sinxcosx)
=2sin2xsinx