证明sina sin(a+2b) - sinb sin(b+2a) =sin(a+b)sin(a-b)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/12 05:09:45

证明：sinasin(a+2b)-sinbsin(b+2a)=sin(a+b)sin(a-b)
sinasin(a+b+b)-sinbsin(a+b+a)=sin(a+b)sin(a-b)
sinasin(a+b)cosb+sinacos(a+b)sinb-sinbsin(a+b)cosa-sinbcos(a+b)sina=sin(a+b)sin(a-b)
sin(a+b)(sinacosb-cosasinb)=sin(a+b)sin(a-b)
sin(a+b)sin(a-b)=sin(a+b)sin(a-b)恒成立
以上各步可逆,证毕

证明sin(a+b)sin(a-b)=(sina+sinb)(sina-sinb) sinb/sina=cos(a+b),证明3sinb=sin(2a+b) 证明sin(2a+b)/sina-2cos(a+b)=sinb/sina 为什么sinA-sinB/sinA+sinB=cos[(A+B)/2]sin[(A-B)/2]/{sin[(A+B)/2 如何证明sin(A-B)*sin(A+B)=sinA²-sinB² 证明sin(a+b)sin(a-b)=sin^2 a-sin^2 b, 如何证明sinA+sinB=2sin((A+B)/2)cos((A-B)/2) 【证明】Sin A+sin B=2Sin 22 sinA-sinB是否等于sin(A-B) 证明三角函数等式sin(A+B)-sinA=2cos(A+B/2)sin(B/2) 求证sin(2A+B)/sinA-2cos(A+B)=sinB/sinA 已知cos(a+B)+1=0,求证sin(2a+B)+sinB=0?(提示:sin(-a)=-sina).