Question

cos（a+b）cos（a-b）=cos2a-sin2b 要换算过程

Answer 1

cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
cos(a-b)=cos(a)cos(b)+sin(a)sin(b)
cos(a+b)cos(a-b)=[cos(a)cos(b)]²-[sin(a)sin(b)]²
由sin²(a)+cos²(a)=1
sin²(b)+cos²(b)=1
消去sin²(a)，cos²(b)，整理得
cos(a+b)cos(a-b)=cos²(a)-sin²(b)

Answer 2

cos（a+b）cos（a-b）=(cosacosb-sinasinb)*(cosacosb+sinasinb)=(cosacosb)^2-(sinasinb)^2=)=(cosacosb)^2-(1-cosa^2)(1-cosb^2)=(cosa^2+cosb^2)-1=(1+2cos2a)/2+(1+2cos2b)/2-1=cos2a+cos2b