sinα =2sin(2a+α ) 求证:tan(a+α)=-3tana
问题描述:
sinα =2sin(2a+α ) 求证:tan(a+α)=-3tana
答
即sin[(a+α)-a]=2sin[(a+α)+a]
sin(a+α)cosa-cos(a+α)sina=2sin(a+α)cosa+2cos(a+α)sina
sin(a+α)cosa=-3cos(a+α)sina
两边除以cosacos(a+α)
sin(a+α)/cos(a+α)=-3cos(a+α)sina/cosa
tan(a+α)=-3tana