Question

cosx=cox3x怎样化简

Answer 1

将cos3x拆成cos2xcosx-sin2xsinx，再拆成cos2xcosx-2sinxcosxsinx。

两边的 cosx约掉，就剩cos2x-2sinxsinx=1

再化简就是4sinxsinx＝0

x＝2kπ

Answer 2

cos3x=cos(x+2x)=cos2xcosx-sin2xsinx
=[2(cosx)^2-1]cosx-2(sinx)^2cosx
所以cosx=[2(cosx)^2-1]cosx-2(sinx)^2cosx
cosx=0或1=2(cosx)^2-1-2(sinx)^2
1=(cosx)^2-2(sinx)^2=cos2x
cos2x=1,或cosx=0
cos2x=1，2x=2kπ
x=kπ
cosx=0,x=kπ+π/2

所以x=kπ/2,k是整数

Answer 3

等式的右边=cos(x+2x)=cos2xcosx-sin2xsinx
=[2(cosx)^2-1]cosx-2(sinx)^2cosx=cosx
则有1)cosx=0可得x=kπ+π/2
2)cosx≠0即x≠kπ+π/2
上等式可化简为2(cosx)^2-1-2(sinx)^2=1
即(cosx)^2-(sinx)^2=1=(cosx)^2+(sinx)^2
也即(sinx)^2=0
则x=2kπ

Answer 4

cos3x=cos(2x+x)=cos2xcosx-sin2xsinx
=(2cosxcosx-1)cosx-2(1-cosxcosx)cosx
代入原式:
cosx=cox3x
cosx=(2cosxcosx-1)cosx-2(1-cosxcosx)cosx
1=2cosxcosx-1-2(1-cosxcosx)
1=2cosxcosx-1-2+2cosxcosx
1=4cosxcosx-3
cosx^2=1

Answer 5

cosx=cos(2x-x)=cos2x*cosx+sin2x*sinx
cos3x=cos(2x+x)=cos2x*cosx-sin2x*sinx
cosx=cos3x化简后得
sin2x*sinx=0