证明:cos(a+b)=cosacosb-sinasinb

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/07/05 12:14:14

证明:cos(a+b)=cosa*cosb-sina*sinb
···不要链接···

2cos(a+b)=exp(i(a+b))+exp(-i(a+b))
=exp(ia)*exp(ib)+exp(-ia)*exp(-ib)
exp(ia)*exp(ib)
(cos(a)+isin(a))(cos(b)+isin(b))
=(cos(a)cos(b)-sin(a)sin(b))+i(sin(a)cos(b)+cos(a)sin(b))
同理
exp(-ia)*exp(-ib)
=(cos(-a)cos(-b)-sin(-a)sin(-b))+i(sin(-a)cos(-b)+cos(-a)sin(-b))
=(cos(a)cos(b)-sin(a)sin(b))-i(sin(a)cos(b)+cos(a)sin(b))
所以
2cos(a+b)=2(cos(a)cos(b)-sin(a)sin(b))
全式除以二即可.

证明:cos(a+b)=cosa*cosb-sina*sinb 已知cos(a-b)=3/1,求(sina+sinb)(sina+sinb)+(cosa+cosb)(cosa+cosb 证明下列恒等式：sin(a+b)*cos(a-b）=sina*cosa+sinb*cosb 求证：cos(a+b)=cosa*cosb-sina*sinb 1,已知:sina+sinB=m,cosa+cosB=n,则cos(a-B)=? 已知sina+sinB=1/2,cosa+cosB=1/3,则cos(a-B)= sinA+sinB+sinC=0,cosA+cosB+cosC=o,则cos(A-B)=______ 已知cosa+cosb=1/2,sina+sinb=1/3,求cos(a-b) 若sina+sinb+siny=cosa+cosb+cosy=0,则cos(a-b)等于已知sinA+sinB=sinC,cosA+cosB=cosC,求cos(A-B)的值若cos（a-b)=1/3,则(sina+sinb)^2+(cosa+cosb)^2= 已知sina+sinb=1,cosa+cosb=0,则cos(a-b)的值为?