sinа=msin(2α+β),求证,tan(α+β)=(1+m)/(1-m)×tanα
问题描述:
sinа=msin(2α+β),求证,tan(α+β)=(1+m)/(1-m)×tanα
答
sinb=msin(2a+b)
sin[(a+b)-a]=msin[(a+b)+a]
sin(a+b)cosa-cos(a+b)sina=m[sin(a+b)cosa+cos(a+b)sina]
(1-m)sin(a+b)cosa=(m+1)cos(a+b)sina
tan(a+b)=(1+m)/(1-m)tana