cos²x*cos²(x/2)-sin²x*sin²(x/2)=cos²x-sin²(x/2)请把过程写出cos²x*cos²(x/2)-sin²x*sin²(x/2)=cos²x-sin²(x/2)请把从左边变到右边的过程写出,

Question

cos²x*cos²(x/2)-sin²x*sin²(x/2)=cos²x-sin²(x/2) 请把过程写出
cos²x*cos²(x/2)-sin²x*sin²(x/2)=cos²x-sin²(x/2) 请把从左边变到右边的过程写出,

Answer 1

cos²x*cos²(x/2)-sin²x*sin²(x/2)
=[cosxcos(x/2)+sinxsin(x/2)][cosxcos(x/2)-sinxsin(x/2)]
=cos(x-x/2)cos(x+x/2)
=cos(x/2)cos(3x/2)
=(1/2)[cos(x/2+3x/2)+cos(3x/2-x/2)]
=(1/2)[cos2x+cosx)
=(1/2)[2cos²x-1+1-2sin²(x/2)]
=(1/2)[2cos²x-2sin²(x/2)]
=cos²x-sin²(x/2)