Question

证明sin(2a+b)/sina-2cos(a+b)=sinb/sina

Answer 1

左边=[sin(2a+b)-2cos(a+b)sina]/sina
=[sina*cos(a+b)+sin(a+b)*cosa-2cos(a+b)sina]/sina
=[sin(a+b)*cosa-cos(a+b)sina]/sina
=sin(a+b-a)/sina
=sinb/sina
=右边
所以结论成立.
逆推法：
sin(2a+b)/sina-2cos(a+b)=sinb/sina
sin(a+a+b)-2cos(a+b)sina=sinb
sinacos(a+b)+cosasin(a+b)-2cos(a+b)sina=sinb
cosasin(a+b)-cos(a+b)sina=sinb
sin(a+b-a)=sinb
sinb=sinb恒成立
以上各步可逆
证毕